DMCA
A Prey Predator Model with Vulnerable Infected Prey Consisting of Non-Linear Feedback (2015)
Citations
286 |
Stability of Motion
- Hahn
- 1967
(Show Context)
Citation Context ... for all initial conditions (0) .nx R Lyapunov function methodology is used for establishing the feedback control of the system (1). By the Lyapunov function methodology, a candidate Lyapunov function is taken as ( ) TV x x Px (2) where P are n n positive definite matrix. Note that : n nV R R is a positive definite function by construction. It is assumed that the parameters of the system (1) are measurable. If a controller u found such that ( ) TV x x Qx (3) where Q are positive definite matrix, then V is a negative definite function. Hence, by Lyapunov stability theory (Hahn, 1967,[34]), the dynamics (1) is globally exponentially stable and hence the condition lim ( ) 0 t x t will be satisfied for all initial conditions (0) .nx R Then the states of the system (1) will be globally asymptotically stable. 3. System Description The model can be written as 2094 Vijaya Lakshmi Gandhavadi Mohan Rao et al. 1 1 1 1 2 2 3 2 1 2 3 2 2 3 3 3 3 2 (1 ) X X rX PX X K X X X PX X X X e X X X dX X X (4) here 1X is the susceptible prey population, 2X is the infected prey, 3X is the predator, r is the growth rate, K the carrying capacity, P the incidence rate,... |
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
5 | Hybrid synchronization of nscroll Chua and Lure chaotic system using backstepping control via novel feedback,” - Suresh, Sundarapandian - 2012 |
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
2 |
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
2 |
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
2 |
Dynamics of a ratio-dependent predator-prey system with a strong Allee effect,
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
2 |
Yang Hui-zhong, Hopf bifurcation in a delayed predatorprey system with modified Leslie-gower and Holling type III schemes, Acta Automatica Sinica,
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
2 |
A food chain model with impulsive perturbations and Holling IV functional response, Chaos, Solitons and Fractals
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
2 |
Rachid Mchich, Tanmay Chwodhury, Gauthier Sallet, Maurice Tchuente, Joydev Chattopadhyay, Effects of disease affecting a predator on the dynamics of a predator-prey system,
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Citation Context ...with functional response, three tropic level food chain system with Holling type IV functional responses, the discrete Nicholson Bailey model with Holling type II functional response and global dynamical behavior of prey-predator system has been revisited. Complex dynamic behavior of three species has been studies. Epidemiology models are routinely used nowadays to understand the spread of infectious diseases with the goal to determine vaccination policies possible to eradicate them, the SIR models, the effect of exotic species on a system of native prey-predator populations has been studied. [23, 24, 25, 26, 27]. The purpose of this paper is to study the dynamics of existence of infected prey effect the prey predator relationship with non-linear feedback control [28- 32]. In this we assumed the susceptible and infected prey populations are predated by predator species by introducing modified Michaelis – Menten – Holling functional response [33]. Various Numerical simulations are then carried out to investigate the relationships between parameters of the model and the effects of the disease on the species. This paper is organized as follows: In section 2 we have given problem statement. In section 3, ... |
2 | Hybrid synchronization of Arneodo and Rossler chaotic systems by active nonlinear control,” - Sundarapandian, Suresh - 2012 |
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Dynamics of a delayed discrete semi-ratio dependent predator-prey system with Holling type IV functional response, Advances in difference equations
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
1 |
Brahampal Singh, Raid Kamel Naji, Dynamical behaviour of two predators competing over a single prey, Biosystems
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
1 |
Brahampal Singh, The dynamics of a food web consisting of two prey and a harvesting predator, Chaos, Solitons and Fractals
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Citation Context ... and their complex properties are the heart of many ecological and biological processes. Predator-prey dynamics 2092 Vijaya Lakshmi Gandhavadi Mohan Rao et al. are well studied in the process of control of some ecosystems. In recent years, a significant number of the published papers on the mathematical discrete time models of biology discussed the system of differential equations and the associated numerical methods. Mathematical models on prey predator systems create a major interest during the last few decades. Study of such system with discrete models and continuous models can be found in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. Discrete time models give rise to more efficient computational models for numerical simulations and it exhibits more plentiful dynamical behaviours than a continuous time model of the same type. The pioneering work of Lotka and Volterra, the theoretical investigation of predator-prey systems in mathematical ecology has advanced greatly. An important extension was carried by Anderson and May, who divided the prey populations into susceptible and infected. One of the important conclusions that were obtained is that the existence of unhealthy prey can destabilized the balance between prey and p... |
1 |
Abdelhadi Abta, Hamad Talibi Alaoui, A comparisonof delayed SIF and SEIR epidemic models, Nonlinear Analysis, Modelling and Control,
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Citation Context ...with functional response, three tropic level food chain system with Holling type IV functional responses, the discrete Nicholson Bailey model with Holling type II functional response and global dynamical behavior of prey-predator system has been revisited. Complex dynamic behavior of three species has been studies. Epidemiology models are routinely used nowadays to understand the spread of infectious diseases with the goal to determine vaccination policies possible to eradicate them, the SIR models, the effect of exotic species on a system of native prey-predator populations has been studied. [23, 24, 25, 26, 27]. The purpose of this paper is to study the dynamics of existence of infected prey effect the prey predator relationship with non-linear feedback control [28- 32]. In this we assumed the susceptible and infected prey populations are predated by predator species by introducing modified Michaelis – Menten – Holling functional response [33]. Various Numerical simulations are then carried out to investigate the relationships between parameters of the model and the effects of the disease on the species. This paper is organized as follows: In section 2 we have given problem statement. In section 3, ... |
1 |
Pramod Kushwah, Chhatrapal Singh Sikarwar, Effect of exotic species on a system of native prey-predator populations: A model,
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Citation Context ...with functional response, three tropic level food chain system with Holling type IV functional responses, the discrete Nicholson Bailey model with Holling type II functional response and global dynamical behavior of prey-predator system has been revisited. Complex dynamic behavior of three species has been studies. Epidemiology models are routinely used nowadays to understand the spread of infectious diseases with the goal to determine vaccination policies possible to eradicate them, the SIR models, the effect of exotic species on a system of native prey-predator populations has been studied. [23, 24, 25, 26, 27]. The purpose of this paper is to study the dynamics of existence of infected prey effect the prey predator relationship with non-linear feedback control [28- 32]. In this we assumed the susceptible and infected prey populations are predated by predator species by introducing modified Michaelis – Menten – Holling functional response [33]. Various Numerical simulations are then carried out to investigate the relationships between parameters of the model and the effects of the disease on the species. This paper is organized as follows: In section 2 we have given problem statement. In section 3, ... |
1 |
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- 2014
(Show Context)
Citation Context ...with functional response, three tropic level food chain system with Holling type IV functional responses, the discrete Nicholson Bailey model with Holling type II functional response and global dynamical behavior of prey-predator system has been revisited. Complex dynamic behavior of three species has been studies. Epidemiology models are routinely used nowadays to understand the spread of infectious diseases with the goal to determine vaccination policies possible to eradicate them, the SIR models, the effect of exotic species on a system of native prey-predator populations has been studied. [23, 24, 25, 26, 27]. The purpose of this paper is to study the dynamics of existence of infected prey effect the prey predator relationship with non-linear feedback control [28- 32]. In this we assumed the susceptible and infected prey populations are predated by predator species by introducing modified Michaelis – Menten – Holling functional response [33]. Various Numerical simulations are then carried out to investigate the relationships between parameters of the model and the effects of the disease on the species. This paper is organized as follows: In section 2 we have given problem statement. In section 3, ... |
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