Control Technique of Maximum Local Lyapunov Exponent on Stable Periodic Solution in Continuous-Time Non-Autonomous Dynamical Systems

We previously proposed a parametric controller to avoid undesirable bifurcations of stable fixed and periodic points in discrete-time dynamical systems. The parameter regulation is derived from an optimization problem on the maximum local Lyapunov exponent and a method of steepest descent. In this paper, on the basis of the ideas and a stroboscopic mapping that transforms the trajectory of a continuous-time periodic solution into a sequence of points, we propose a technique to control the maximum local Lyapunov exponent on stable periodic oscillations in continuous-time non-autonomous dynamical systems.

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