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Global Asymptotic Stability in a Nonautonomous nSpecies LotkaVolterra PredatorPrey System with Infinite Delays
, 2001
"... In this paper, a delayed nspecies nonautonomous LotkaVolterra type foodchain system without dominating instantaneous negative feedback is investigated. By means of a Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solution of the system. ..."
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In this paper, a delayed nspecies nonautonomous LotkaVolterra type foodchain system without dominating instantaneous negative feedback is investigated. By means of a Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solution of the system
LOTKAVOLTERRA SYSTEMS WITH DELAY
"... Sufftcient conditions for a LotkaVolterra competitive delay system to be permanent and its positive equilibrium point to be a global attractor are given. ..."
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Sufftcient conditions for a LotkaVolterra competitive delay system to be permanent and its positive equilibrium point to be a global attractor are given.
Partial Survival and Extinction of Species in Nonautonomous LotkaVolterra Systems with Delays
"... Consider the extinction of species in models governed by the following nonautonomous LotkaVolterra system with delays: dxi(t) dt = xi(t){ci(t)− n∑ j=1 m∑ l=0 alij(t)xj(t − τl)}, t ≥ t0, 1 ≤ i ≤ n, xi(t) = φi(t) ≥ 0, t ≤ t0, and φi(t0)> 0, 1 ≤ i ≤ n, where each φi(t) is a continuous function f ..."
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Consider the extinction of species in models governed by the following nonautonomous LotkaVolterra system with delays: dxi(t) dt = xi(t){ci(t)− n∑ j=1 m∑ l=0 alij(t)xj(t − τl)}, t ≥ t0, 1 ≤ i ≤ n, xi(t) = φi(t) ≥ 0, t ≤ t0, and φi(t0)> 0, 1 ≤ i ≤ n, where each φi(t) is a continuous function
Global Stability for Nspecies LotkaVolterra Systems with Delay, II: Reducible Cases, Sufficiency and Necessity 1)
"... Abstract. in this paper, an nspecies delayed LotkaVolterra system without delayed intraspecific competitions is considered. It is proved that the system is globally stable for all offdiagonal delays τij ≥ 0 if and only if the interaction matrix A of the system satisfies Condition (WDD). 1. ..."
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Abstract. in this paper, an nspecies delayed LotkaVolterra system without delayed intraspecific competitions is considered. It is proved that the system is globally stable for all offdiagonal delays τij ≥ 0 if and only if the interaction matrix A of the system satisfies Condition (WDD). 1.
Persistence and global stability for discrete models of nonautonomous LotkaVolterra type
 J. Math. Anal. Appl
"... Consider the persistence and the global asymptotic stability of the following discrete model of puredelay nonautonomous LotkaVolterra type: Ni(p+ 1) = Ni(p) exp{ci(p)− n∑ j=1 m∑ l=0 alij(p)Nj(p − kl)}, p = 0, 1, 2, · · · , 1 ≤ i ≤ n, Ni(p) = Ni,p ≥ 0, p ≤ 0, and Ni,0> 0, 1 ≤ i ≤ n, where ..."
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Consider the persistence and the global asymptotic stability of the following discrete model of puredelay nonautonomous LotkaVolterra type: Ni(p+ 1) = Ni(p) exp{ci(p)− n∑ j=1 m∑ l=0 alij(p)Nj(p − kl)}, p = 0, 1, 2, · · · , 1 ≤ i ≤ n, Ni(p) = Ni,p ≥ 0, p ≤ 0, and Ni,0> 0, 1 ≤ i ≤ n, where
Global stability in discrete models of nonautonomous LotkaVolterra type
"... In this paper, we establish sufficient conditions for the global asymptotic stability of the following discrete models of nonautonomous LotkaVolterra type: Ni(p+ 1) = Ni(p) exp{ci(p) − ai(p)Ni(p)− n∑ j=1 m∑ l=0 alij(p)Nj(p − kl)}, 1 ≤ i ≤ n, for p = 0, 1, 2, · · ·, Ni(p) = Nip ≥ 0, for p ≤ 0, ..."
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In this paper, we establish sufficient conditions for the global asymptotic stability of the following discrete models of nonautonomous LotkaVolterra type: Ni(p+ 1) = Ni(p) exp{ci(p) − ai(p)Ni(p)− n∑ j=1 m∑ l=0 alij(p)Nj(p − kl)}, 1 ≤ i ≤ n, for p = 0, 1, 2, · · ·, Ni(p) = Nip ≥ 0, for p ≤ 0
doi:10.1093/imamat/hxv002 Global asymptotic stability of stochastic Lotka–Volterra
, 2015
"... systems with infinite delays ..."
Results 1  10
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