Synchronization and stabilization of Multi-scroll Integer and fractional Order Chaotic attractors Generated using trigonometric Functions

Sigmoidal functions are usually used to characterize the behavior of dynamical systems, in particular, for neural networks. Recently, multilevel piecewise linear functions have been employed in cellular neural networks (CNN). In this paper, we first use the inverse trigonometric function, tan−1(x), to generate a series of trigonometric functions to obtain one-, twoand three-directional multi-scroll integer and fractional order chaotic attractors. Then, based upon the properties of the chaotic systems, simple feedback control laws are designed to stabilize or synchronize the integer and fractional order chaotic systems. Numerical simulations are presented to demonstrate the applicability of theoretical predictions.