منابع مشابه
Equivariant Hopf bifurcation for functional differential equations of mixed type
In this paper we employ the Lyapunov–Schmidt procedure to set up equivariant Hopf bifurcation theory of functional differential equations of mixed type. In the process we derive criteria for the existence and direction of branches of bifurcating periodic solutions in terms of the original system, avoiding the process of center manifold reduction. © 2010 Elsevier Ltd. All rights reserved.
متن کاملOscillator death in coupled functional differential equations near Hopf bifurcation
The stability of the equilibrium solution is analyzed for coupled systems of retarded functional differential equations near a supercritical Hopf bifurcation. Necessary and sufficient conditions are derived for asymptotic stability under general coupling conditions. It is shown that the largest eigenvalue of the graph Laplacian completely characterizes the effect of the connection topology on t...
متن کاملHopf Bifurcation Analysis of Distributed Delays Equations
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.
متن کاملHopf bifurcation formula for first order differential-delay equations
This work presents an explicit formula for determining the radius of a limit cycle which is born in a Hopf bifurcation in a class of first order constant coefficient differential-delay equations. The derivation is accomplished using Lindstedt s perturbation method. 2005 Elsevier B.V. All rights reserved. PACS: 02.30.Ks; 02.30.Oz
متن کاملHOPF BIFURCATION CONTROL WITH PD CONTROLLER
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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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1980
ISSN: 0022-247X
DOI: 10.1016/0022-247x(80)90113-4