This paper investigates the chaos synchronization problem for a class of uncertain master–slave unified chaotic systems. Based on the sliding mode control technique, a robust control scheme is established which guarantees the occurrence of a sliding motion of error states even when the parameter uncertainty and external perturbation are present. Furthermore, a novel proportional–integral (PI) s...

The nonlinear behavior analysis and chaos control for Duffing-Holmes chaotic system is discussed in the paper. In order to suppress the irregular chaotic motion, an optimal backstepping controller is designed. The backstepping method consists of parameters with positive values. The improper selection of the parameters leads to inappropriate responses or even may lead to instability of the syste...

‎in this paper, we investigate the chaotic behaviors of the fractional-order permanent magnet synchronous motor (pmsm) system. the necessary condition for the existence of chaos in the fractional-order pmsm system is deduced and an active controller is developed based on the stability theory for fractional systems. the presented control scheme  is simple and flexible, and it is suitable both fo...

This paper reports the finding of a simple one-parameter family of three-dimensional quadratic autonomous chaotic systems. By tuning the only parameter, this system can continuously generate a variety of cascading Lorenz-like attractors, which appears to be richer than the unified chaotic system that contains the Lorenz and the Chen systems as its two extremes. Although this new family of chaot...

in this work, different types of chaotic 1-manifolds which lie on the chaotic spheres or on a torus are introduced. some types of retractions of the chaotic spheres affect on the 1-chaotic systems, and other types of retractions occur to the geometric manifold but make the 1-chaotic manifold invariant. the existed retractions are discussed through new proved theorems. also we construct diffe...

In this article a non-autonomous unified chaotic system with continuous periodic switch between the Chen and Lorenz systems is introduced. Dynamical behaviors of this system are investigated. We consider the identical (complete) synchronization of the bi-directionally coupled between two identical systems of this type and then analyze its stability by estimating the entire Lyapunov characterist...