Hybrid Projective Synchronization of 4-D Hyperchaotic Systems via Adaptive Control

Abstract

This paper designs a procedure for investigating the hybrid projective synchronization (HPS) scheme between two identical 4-D hyperchaotic systems. Based on Lyapunov stability theory (LST), an adaptive control technique (ACT) has been designed to achieve the desired HPS scheme. The suggested technique determines globally the asymptotic stability and identification of parameters simultaneously using HPS scheme. It is noted that complete , hybrid and anti-synchronization turns into particular cases of HPS scheme. Numerical simulations are presented to validate the effectivity and feasibleness of the considered technique by using MATLAB. Remarkably, the theoretical and computational outcomes are in complete agreement. Also, the considered HPS scheme is very efficient as it has numerous applications in encryption and secure communication.

Effect of Different Forms of Periodic Piecewise Linear Forces on Duffing Oscillator

“…Compared to harmonic forces, these forces are effectively used to stabilize some nonlinear systems with a relatively low frequency of fast oscillations. Up to now, a variety of control methods to achieve chaos control have been introduced in control theory such as parametric modulation [26], active control [29], adaptive control [30], backstepping design [31], feedback control [32], sliding mode control [33], impulsive control [34], etc. In this study, we also address the problem of chaos suppression by an ε-parametric control force defined for one of the periodic piecewise linear forces, which is less studied in the present literatures.…”