Weak tracking in nonautonomous chaotic systems

Chaotic Dynamics in Nonautonomous Maps: Application to the Nonautonomous Hénon Map

Chaotic Behavior in Nonautonomous Equations without Any Time Periodicity

We investigate chaotic behavior of ordinary differential equations with a homoclinic orbit to a dissipative saddle point under a general time dependent forcing without any periodicity in time. We study Poincaré return maps in extended phase space, introducing a characteristic function that generalizes the classic Melnikov function. We then show that the dynamics of the solutions of these equati...

Delayed feedback control of periodic orbits without torsion in nonautonomous chaotic systems: theory and experiment.

We demonstrate theoretically and experimentally that the unstable delayed feedback controller is an efficient tool for stabilizing torsion-free unstable periodic orbits in nonautonomous chaotic systems. To improve the global control performance we introduce a two-step control algorithm. The problem of a linear stability of the system under delayed feedback control is treated analytically. Theor...

On the shadowing property of nonautonomous discrete systems

In this paper we study shadowing property for sequences of mappings on compact metric spaces, i.e. nonautonomous discrete dynamical systems. We investigate the relation of  weak contractions with shadowing and h-shadowing property.

Nonautonomous pulse-driven chaotic oscillator based on Chua's circuit

A novel nonautonomous chaotic oscillator based on the passive structure of Chua's circuit is proposed. Unlike most of the available members of this class of chaotic oscillators, the proposed circuit is driven by a periodic bipolar pulse-train rather than by sinusoidal excitation. This results in equilibrium points which have ®xed positions in space. The circuit employs self feedback via a singl...