## Control of Hopf bifurcation in autonomous system based on washout filter.(English)Zbl 1397.34077

Summary: In order to further understand a Lorenz-like system, we study the stability of the equilibrium points and the existence of Hopf bifurcation by center manifold theorem and normal form theory. More precisely, we designed a washout controller such that the equilibrium $$E_0$$ undergoes a controllable Hopf bifurcation, and by adjusting the controller parameters, we delayed Hopf bifurcation phenomenon of the equilibrium $$E_+$$. Besides, numerical simulation is given to illustrate the theoretical analysis. Finally, two possible electronic circuits are given to realize the uncontrolled and the controlled systems.

### MSC:

 34C60 Qualitative investigation and simulation of ordinary differential equation models 34H05 Control problems involving ordinary differential equations 34C23 Bifurcation theory for ordinary differential equations 34C20 Transformation and reduction of ordinary differential equations and systems, normal forms 34D45 Attractors of solutions to ordinary differential equations 94C05 Analytic circuit theory
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