HOPF BIFURCATION CONTROL WITH PD CONTROLLER

Authors

  • H.M. MOHAMMADINEJAD DEPARTMENT OF MATHEMATICS, FACULTY OF MATHEMATICS AND STATISTICS, UNIVERSITY OF BIRJAND, BIRJAND, IRAN
  • M. Darvishi DEPARTMENT OF MATHEMATICS, FACULTY OF MATHEMATICS AND STATISTICS, UNIVERSITY OF BIRJAND, BIRJAND, IRAN
Abstract:

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 model as operator Equation, apply orthogonal decomposition, compute the center manifold and normal form we determined the direction and stability of bifurcating periodic solutions. Therefore the Hopf bifurcation of the model became controllable to achieve desirable behaviour which are applicable in certain circumstances.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Delayed Feedback Control near Hopf Bifurcation

The stability of functional differential equations under delayed feedback is investigated near a Hopf bifurcation. Necessary and sufficient conditions are derived for the stability of the equilibrium solution using averaging theory. The results are used to compare delayed versus undelayed feedback, as well as discrete versus distributed delays. Conditions are obtained for which delayed feedback...

full text

Hopf Bifurcation Control of a Lorenz-Like System Based on Washout Filter Controller

About a three-dimensional autonomous continuous Lorenz-like system. Through the full analysis of equilibrium points, we can derive the parameter condition of Hopf bifurcation; Next we adopt a Washout filter controller designed independently to control the Hopf bifurcation of the system, and the effect of the controller’s parameters on the position of bifurcation point, the bifurcation type, and...

full text

Hopf Bifurcation with Dn-symmetry

The aim of this paper is to study Hopf bifurcation with Dn-symmetry assuming Birkhoff normal form. We consider the standard action of Dn on C. This representation is absolutely irreducible and so the corresponding Hopf bifurcation occurs on C ⊕ C. Golubitsky and Stewart (Hopf bifurcation with dihedral group symmetry: Coupled nonlinear oscillators. In: Multiparameter Bifurcation Series (M. Golub...

full text

Hamiltonian Hopf bifurcation with symmetry

In this paper we study the appearance of branches of relative periodic orbits in Hamiltonian Hopf bifurcation processes in the presence of compact symmetry groups that do not generically exist in the dissipative framework. The theoretical study is illustrated with several examples.

full text

Hopf bifurcation Control Using Nonlinear Feedback with Polynomial Functions

A general explicit formula is derived for controlling bifurcations using nonlinear state feedback. This method does not increase the dimension of the system, and can be used to either delay (or eliminate) existing bifurcations or change the stability of bifurcation solutions. The method is then employed for Hopf bifurcation control. The Lorenz equation and Rössler system are used to illustrate ...

full text

Ikeda Hopf bifurcation revisited

A large variety of passive optical systems subject to a delayed feedback have appeared in the literature and are described mathematically by the same class of scalar delay differential equations (DDEs). These equations include Ikeda DDE and their solutions are determined in terms of a control parameter distinct from the delay. We concentrate on the first Hopf bifurcation generated by a fixed de...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 4  issue 2

pages  51- 57

publication date 2015-08-01

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023