Hopf bifurcation formula for first order differential-delay equations
نویسندگان
چکیده
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
منابع مشابه
BIFURCATION ANALYSIS OF A DDE MODEL OF THE CORAL REEF
In this paper, first we discuss a local stability analysis of model was introduced by P. J. Mumby et. al. (2007), with $frac{gM^{2}}{M+T}$ as the functional response term. We conclude that the grazing intensity is the important parameter to control the existence or extinction of the coral reef. Next, we consider this model under the influence of the time delay as the bifurcat...
متن کاملDelay Induced Subcritical Hopf Bifurcation in a Diffusive Predator-prey Model with Herd Behavior and Hyperbolic Mortality∗
In this paper, we consider the dynamics of a delayed diffusive predator-prey model with herd behavior and hyperbolic mortality under Neumann boundary conditions. Firstly, by analyzing the characteristic equations in detail and taking the delay as a bifurcation parameter, the stability of the positive equilibria and the existence of Hopf bifurcations induced by delay are investigated. Then, appl...
متن کاملBifurcations in Delay Differential Equations and Applications to Tumor and Immune System Interaction Models
In this paper, we consider a two-dimensional delay differential system with two delays. By analyzing the distribution of eigenvalues, linear stability of the equilibria and existence of Hopf, Bautin, and Hopf–Hopf bifurcations are obtained in which the time delays are used as the bifurcation parameter. General formula for the direction, period, and stability of the bifurcated periodic solutions...
متن کاملThreshold harvesting policy and delayed ratio-dependent functional response predator-prey model
This paper deals with a delayed ratio-dependent functional response predator-prey model with a threshold harvesting policy. We study the equilibria of the system before and after the threshold. We show that the threshold harvesting can improve the undesirable behavior such as nonexistence of interior equilibria. The global analysis of the model as well as boundedness and permanence properties a...
متن کاملEquivariant Hopf Bifurcation in a Ring of Identical Cells with Delay
A kind of delay neural network with n elements is considered. By analyzing the distribution of the eigenvalues, a bifurcation set is given in an appropriate parameter space. Then by using the theory of equivariant Hopf bifurcations of ordinary differential equations due to Golubitsky et al. 1988 and delay differential equations due to Wu 1998 , and combining the normal form theory of functional...
متن کامل