ON DYNAMICAL SYSTEMS GENERATED BY TWO ALTERNATING VECTOR FIELDS

Dynamical systems with time evolution determined by two alternating vector fields are investigated both analytically and numerically. When the two vector fields are related by an involutory diffeomorphism G then the fixed points of G (either isolated or non-isolated) are shown to give rise to branches of periodic solutions of the resulting non-autonomous system. The method of averaging is used for small switching periods. Detailed numerical study of both conservative (“blinking vortex”) and dissipative (“blinking nodes”, “blinking cycles” and “blinking Lorenz”) systems shows that the technique of blinking can be used to initiating and controlling of chaos.

CONTROLLING OF CHAOS IN THE DRIVEN CHUA'S CIRCUIT

The nonautonomous version of Chua's circuit can exhibit a wide variety of bifurcation routes to chaos. In this paper we explore the possibility of controlling chaos in this circuit by the addition of a second periodic signal for certain parametric choices.

CONTROLLING OF CHAOS IN BONHOEFFER- VAN DER POL OSCILLATOR

In this letter controlling of chaos in Bonhoeffer-van der Pol oscillator is investigated using various different control algorithms. Specifically, using an adaptive control algorithm we analyse the resetting of the system dynamics from a chaotic attractor to a limit cycle attractor. We demonstrate that, starting from a chaotic regime, it is possible to bring the system to a regular regime by means of a small parametric perturbation as well as by the addition of a weak external force. It is then shown that one can eliminate chaotic evolution by stabilizing an unstable periodic orbit by making small adjustments to an external parameter. Finally, we show the suppression of chaos by adding appropriate external noise.