The paper deals with the problem of estimation of the topological entropy for non-autonomous systems of differential equations via the second (direct) Lyapunov method. The main result of the paper is illustrated by examples concerning the Lorenz system and Duffing oscillator.

In this paper, we investigate the existence and uniqueness of almost periodic solutions for a class of nonlinear Duffing system with time-varying delays. By using theory of exponential dichotomies and contraction mapping principle, we establish some new results and give an example to illustrate the theoretical analysis in this work.

TheDuffing oscillator has become a classical paradigm for illustrating the remarkable jump phenomenon and other nonlinear behaviour [1,2]. The understanding gained on the basis of this low-order nonlinear systemhas helped in the development of reducedorder models of complex mechanical systems ranging from microscales to macroscales [3,4]. The nondimensional Duffing equation with damping and ext...

We investigate a modified Murali-Lakshmanan-Chua(MLC) circuit in which the Chua’s diode is replaced with a negative conductance and pair of diode as a nonlinearity. The dual nature of this circuit exhibiting the rich dynamics of both the MLC circuit and the Duffing van der Pol is also explored. The performance of the circuit is investigated by means of laboratory experiments, numerical integrat...

The chaotic synchronization regime in coupled dynamical systems is considered. It has been shown that the onset of a synchronous regime is based on the appearance of a phase relation between the interacting chaotic oscillator frequency components of Fourier spectra. The criterion of synchronization of spectral components as well as the measure of synchronization has been discussed. The universa...

This paper presents a fuzzy controller to solve a master-slave chaos synchronization problem. At first, the method of traditional sliding mode control is considered, which utilizes the discontinuous sign function to make the system state reaching a sliding surface. Next, fuzzy rules are determined according to the Lyapunov theorem, and the fuzzy controller is designed for chaos synchronization....

The problem of hybrid chaos synchronization is investigated, where a digital response subsystem is designed to synchronize with an analog drive subsystem. The approach taken is a new prediction-based digital redesign for a continuous-time observer embedded in the response via an optimal linearization approach of the nonlinear chaotic systems. Three typical but topologically quite different chao...