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Oscillation Theory for Second Order Dynamic Equations
 of Series in Mathematical Analysis and Applications. Taylor and Francis Ltd
, 2003
"... There are numerous books on oscillation theory for differential equations such as [1, 2, 5, 6], to name but a few. The monograph by Agarwal, Grace, and O’Regan is an excellent addition to the existing literature. It covers topics related to oscillation theory for differential equations with deviatin ..."
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Cited by 13 (3 self)
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There are numerous books on oscillation theory for differential equations such as [1, 2, 5, 6], to name but a few. The monograph by Agarwal, Grace, and O’Regan is an excellent addition to the existing literature. It covers topics related to oscillation theory for differential equations with deviating arguments, neutral functional differential equations, second order ordinary differential equations, and impulsive differential equations. This book is very well organized; being in the classical mathematical style, the presented material is divided into definitions, theorems, proofs, lemmas, remarks, and examples. It is selfcontained and consistent, and it is easy to follow the presentation. Only some background in calculus and differential equations is required. One definitely does not have to be a differential equations specialist in order to follow this wellwritten compact but thorough treatment. In an effort to make this book available to a wide audience of scientists, a first chapter collects some basic results for second order linear
Nonmonotone travelling waves in a single species reactiondiffusion equation with delay
 J. Differential Equations
"... We prove the existence of a continuous family of positive and generally nonmonotone travelling fronts in delayed reactiondiffusion equations ut(t, x) = ∆u(t, x) − u(t, x) + g(u(t − h, x)) (∗), when g ∈ C 2 (R+, R+) has exactly two fixed points: x1 = 0 and x2 = a> 0. Recently, nonmonotonic waves ..."
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Cited by 10 (3 self)
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We prove the existence of a continuous family of positive and generally nonmonotone travelling fronts in delayed reactiondiffusion equations ut(t, x) = ∆u(t, x) − u(t, x) + g(u(t − h, x)) (∗), when g ∈ C 2 (R+, R+) has exactly two fixed points: x1 = 0 and x2 = a> 0. Recently, nonmonotonic waves were observed in numerical simulations by various authors. Here, for a wide range of parameters, we explain why such waves appear naturally as the delay h grows. For the case of g with negative Schwarzian, our conditions are rather optimal; we observe that the well known MackeyGlass type equations with diffusion fall within this subclass of (∗). As an example, we consider the diffusive Nicholson’s blowflies equation. 1.
New congestion control schemes over wireless networks: Stability analysis
 in Proceedings of the 16 th IFAC World Congress
, 2005
"... Abstract: This paper proposes two new congestion control schemes for packet switched wireless networks. Starting from the seminal work of Kelly (Kelly et al., Dec 1999), we consider the decentralized flow control model for a TCPlike scheme and extend it to the wireless scenario. Motivated by the pr ..."
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Cited by 7 (5 self)
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Abstract: This paper proposes two new congestion control schemes for packet switched wireless networks. Starting from the seminal work of Kelly (Kelly et al., Dec 1999), we consider the decentralized flow control model for a TCPlike scheme and extend it to the wireless scenario. Motivated by the presence of channel errors, we introduce updates in the part of the model representing the number of connections the user establishes with the network; this assumption has important physical interpretation. Specifically, we propose two updates: the first is static, while the second evolves dynamically. The global stability of both schemes has been proved; also, a stochastic stability study and the rate of convergence of the two algorithms have been investigated. This paper focuses on the delay sensitivity of both schemes. A stability condition on the parameters of the system is introduced and proved. Moreover, some deeper insight on the structure of the oscillations of the system is attained. To support the theoretical results, simulations are provided. Copyright c○2005 IFAC
Some oscillation criteria for first order delay dynamic equations
 Far East J. Appl. Math
, 2005
"... Abstract: We present an oscillation criterion for first order delay dynamic equations on time scales, which contains wellknown criteria for delay differential equations and delay difference equations as special cases. We illustrate our results by applying them to various kinds of time scales. ..."
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Cited by 6 (1 self)
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Abstract: We present an oscillation criterion for first order delay dynamic equations on time scales, which contains wellknown criteria for delay differential equations and delay difference equations as special cases. We illustrate our results by applying them to various kinds of time scales.
Low Frequency Fluctuations and Multimode Operation of a Semiconductor Laser With Optical Feedback
, 1998
"... Z. We experimentally investigate low frequency fluctuations LFF in a FabryPerot semiconductor laser with optical feedback from an external mirror. During LFF, the time resolved optical spectrum shows that many longitudinal modes of the solitary laser enter into the transients. After each LFF event, ..."
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Cited by 3 (0 self)
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Z. We experimentally investigate low frequency fluctuations LFF in a FabryPerot semiconductor laser with optical feedback from an external mirror. During LFF, the time resolved optical spectrum shows that many longitudinal modes of the solitary laser enter into the transients. After each LFF event, the excited solitarylaser modes recover similarly. However, the recovery for the power in each mode is much slower than the recovery of the total power. The intermode exchange of energy during the recovery indicates that a singlelongitudinal mode description of such LFF behavior will not capture important underlying dynamics. The relevance of multimode dynamics is confirmed in a feedback experiment where the external mirror is substituted by a diffraction grating. q 1998 Elsevier Science B.V. The effect of delayed feedback on dynamical systems has been studied in different branches of science such as wx wx wx physics 1 , chemistry 2 and other fields 3 . These systems, which are commonly ...
OSCILLATION CRITERIA FOR CERTAIN THIRD ORDER NONLINEAR DIFFERENCE EQUATIONS
"... doi:10.2298/AADM0901027G ..."
Temporal Dynamics of Semiconductor Lasers with Optical Feedback
"... We measure the temporal evolution of the intensity of an edge emitting semiconductor laser with delayed optical feedback for time spans ranging from 4.5 to 65 ns with a time resolution from 16ps to 230ps respectively. Spectrally resolved streak camera measurements show that the fast pulsing of th ..."
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We measure the temporal evolution of the intensity of an edge emitting semiconductor laser with delayed optical feedback for time spans ranging from 4.5 to 65 ns with a time resolution from 16ps to 230ps respectively. Spectrally resolved streak camera measurements show that the fast pulsing of the total intensity is a consequence of the time delay and multimode operation of the laser. We experimentally observe that the instabilities at low frequency are generated by the interaction among different modes of the laser. PACS numbers: 05.40.+j, 05.90.+m, 42.60.Mi Typeset using REVT E X 1 Nonlinear systems with delayed feedback are of actual interest because they can be widely found in economy, biology, chemistry and physics [1]. These systems are in principle infinite dimensional, and from this point of view, it is difficult to classify them a priori as deterministic dynamical systems because the existence and unicity of a solution has to be demonstrated for each particular mode...
A Backward Time Shift Filter for Nonlinear DelayedFeedback Systems
, 2001
"... Using a simple nonlinear filter, it is possible to shift arbitrarily complex wave forms produced by systems with a delayed feedback backwards in time. Physically, this corresponds to a seemingly noncausal transmission of signals. Filter chains allow for signals travelling against the coupling direct ..."
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Cited by 2 (2 self)
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Using a simple nonlinear filter, it is possible to shift arbitrarily complex wave forms produced by systems with a delayed feedback backwards in time. Physically, this corresponds to a seemingly noncausal transmission of signals. Filter chains allow for signals travelling against the coupling direction of the chain. These apparent paradoxes are resolved, and possible physical implications are discussed. 2001 Elsevier Science B.V. All rights reserved. PACS : 02.30.Ks; 05.45.a; 47.52.+j; 42.65.Sf Keywords: Delayed feedback; Nonlinear filtering; Signal transmission; Chaos; Causality 1. Introduction Systems with a nonlinear timedelayed feedback are quite ubiquitous in nature and technology. Already in linear systems a delayed feedback can cause instabilities leading to complex oscillations. In nature, time delays are mostly caused by finite signal transmission speeds and memory effects. A famous example is the oscillatory behaviour of the pupil light reflex which can be understood u...
Nonlinear Oscillations and Chaos in Chemical Cardiorespiratory Control
, 1995
"... We report progress made on an analytic investigation of lowfrequency cardiorespiratory variability in humans. The work is based on an existing physiological model of chemicallymediated bloodgas control via the central and peripheral chemoreceptors, that of Grodins, Buell & Bart (1967). Scaling an ..."
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Cited by 2 (2 self)
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We report progress made on an analytic investigation of lowfrequency cardiorespiratory variability in humans. The work is based on an existing physiological model of chemicallymediated bloodgas control via the central and peripheral chemoreceptors, that of Grodins, Buell & Bart (1967). Scaling and simplification of the Grodins model yields a rich variety of dynamical subsets; the thesis focusses on the dynamics obtained under the normoxic assumption (i.e., when oxygen is decoupled from the system). In general, the method of asymptotic reduction yields submodels that validate or invalidate numerous (and more heuristic) extant efforts in the literature. Some of the physiologicallyrelevant behaviour obtained here has therefore been reported before, but a large number of features are reported for the first time. A particular novelty is the explicit demonstration of cardiorespiratory coupling via chemosensory control. The physiology and literature reviewed in Chapters 1 and 2 set the stage for the investigation. Chapter 3 scales and simplifies the Grodins model; Chapters 4, 5, 6 consider carbon dioxide dynamics at the central chemoreceptor. Chapter 7 begins analysis
Bifurcation analysis in a delayed diffusive Nicholson’s blowflies equation ∗
"... The dynamics of a diffusive Nicholson’s blowflies equation with a finite delay and Dirichlet boundary condition have been investigated in this paper. The occurrence of steady state bifurcation is proved by applying phase plane ideas. The existence of Hopf bifurcation at the positive equilibrium is o ..."
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The dynamics of a diffusive Nicholson’s blowflies equation with a finite delay and Dirichlet boundary condition have been investigated in this paper. The occurrence of steady state bifurcation is proved by applying phase plane ideas. The existence of Hopf bifurcation at the positive equilibrium is obtained, and the phenomenon that the unstable positive equilibrium state without dispersion may become stable with dispersion under certain conditions is found by analyzing the distribution of the eigenvalues. By the theory