In this paper, the control of chemical chaotic dynamical system is investigated by time-delayed feedback control technique.The controllability and the stability of the equilibriums and local Hopf bifurcation of the system are verified. Some numerical simulations which show the effectiveness of the time-delayed feedback control method are provided.
In this paper, a Duffing oscillator model with delayed velocity feedback is considered. Applying the time delayed feedback control method and delayed differential equation theory, we establish some criteria which ensure the stability and the existence of Hopf bifurcation of the model. By choosing the delay as bifurcation parameter and analyzing the associated characteristic equation,the existence of bifurcation parameter point is determined. We found that if the time delay is chosen as a bifurcation parameter,Hopf bifurcation occurs when the time delay is changed through a series of critical values. Some numerical simulations show that the designed feedback controllers not only delay the onset of Hopf bifurcation, but also enlarge the stability region for the model.
In this paper, bifurcations of limit cycles at three fine focuses for a class of Z2-equivariant non-analytic cubic planar differential systems axe studied. By a transformation, we first transform non- analytic systems into analytic systems. Then sufficient and necessary conditions for critical points of the systems being centers are obtained. The fact that there exist 12 small amplitude limit cycles created from the critical points is also proved. Henceforth we give a lower bound of cyclicity of Z2-equivaxiant non-analytic cubic differential systems.
In this paper, the problem of controlling chaos in a Sprott E system with distributed delay feedback is considered. By analyzing the associated characteristic transcendental equation, we focus on the local stability and Hopf bifurcation nature of the Sprott E system with distributed delay feedback. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions are derived by using the normal form theory and center manifold theory. Numerical simulations for justifying the theoretical analysis are provided.
