Abstract
In this paper Hopf bifurcation control is implemented in order to change the bifurcation from supercritical to subcritical in a differential equations system of Lorenz type. To achieve this purpose: first, a region of parameters is identified where the system has a supercritical Hopf bifurcation; second, a class of non-linear feedback control laws is proposed; finally, it is shown that there are control laws which the disturbed system undergoes subcritical Hopf bifurcation.
Highlights
In [1] the Bifurcation Control is described as the task of designing a control law that modifies the bifurcation characteristics in order to achieve a desirable dynamic behaviour
It will be demonstrated that Hopf bifurcation is supercritical, at verifying that the first Lyapunov coefficient is negative in the equilibrium point P1
Problem consists in finding a control law of the class (11) such that the perturbed system preserves the equilibrium points of the system (3), it presents Hopf bifurcation and this is subcritical
Summary
In [1] the Bifurcation Control is described as the task of designing a control law that modifies the bifurcation characteristics in order to achieve a desirable dynamic behaviour. When the system (1) presents Hopf bifurcation in a equilibrium point ( ) x∗,α , the Hopf Bifurcation Control consists in to determine a control law ( ) u ⋅,α 0 of a parametric class u (⋅,α ) , in such a way that the equilibrium point ( ) ( ) x∗,α of (1) moves to an equilibrium point x0,α 0 of the perturbed system (2), the Hopf bifurcation is preserved and one of the following situations occurs: 1) Stability of the limit cycle that emerges from the Hopf bifurcation changes from unstable to stable or vice versa. The objective is apply Hopf Bifurcation Control to the system (3) in order to change the Hopf bifurcation from supercritical to subcritical, by using non-lineal control laws in state feedback.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
