منابع مشابه
Bifurcation analysis of chemical reaction mechanisms. II. Hopf bifurcation analysis
Oneand two-parameter Hopf bifurcation behavior is analyzed for several variants of the Citri-Epstein mechanism of the chlorite-iodide reaction. The coefficients of an equation for the amplitude of oscillations (the universal unfolding of the Hopf bifurcation) are evaluated numerically. Local bifurcation diagrams and bifurcation sets are derived from the amplitude equation. Suband supercritical ...
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Since the pioneering work of Lorenz [1] and Rössler [2], it has been known that chaos can occur in systems of autonomous ordinary differential equations with as few as three variables and one or two quadratic nonlinearities. Many other chaotic systems have been discovered over the last years [3–7]. There have been extensive investigations on dynamical behaviors of these chaotic systems [8–14]. ...
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In this paper, we investigate the problem of bifurcation control for a delayed logistic growth model. By choosing the timedelay as the bifurcation parameter, we present a Proportional - Derivative (PD) Controller to control Hopf bifurcation. We show that the onset of Hopf bifurcation can be delayed or advanced via a PD Controller by setting proper controlling parameter. Under consideration mode...
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Delay in dynamical systems is exhibited whenever the system’s behavior is dependent at least in part on its history. Many technological and biological systems are known to exhibit such behavior; coupled laser systems, high-speed milling, population dynamics and gene expression are some examples of delayed systems. This work analyzes a simple differential delay equation that is motivated by a sy...
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In this article, we develop a modified version of the graphical Hopf bifurcation theorem for capturing smooth oscillations of delay differential equations with distributed delays. Our approach relies on a simple interpretation of the effect of the distributed delay based on the Laplace transform. The theoretical results are illustrated with an example of neural networks.
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ژورنال
عنوان ژورنال: International Journal of Pure and Apllied Mathematics
سال: 2015
ISSN: 1311-8080,1314-3395
DOI: 10.12732/ijpam.v104i1.1