Controlling Chaos in a Newly Designed Chaotic Hamiltonian System Based on Hénon-Heiles Model using Active Controlled Hybrid Projective Synchronization

In this paper, a systematic approach is designed for investigating the hybrid projective synchronization (HPS) in identical chaotic Hamiltonian systems based on Hénon-Heiles Model by using active control method (ACM). Initially, an active control law is described to achieve asymptotic stability of state vectors of given system using Lyapunov stability theory (LST). Additionally, numerical simulations utilizing MATLAB toolbox are presented to validate the efficiency and effectiveness of the designed approach. Furthermore, the proposed strategy has numerous applications in encryption and secure communication.

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

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.

The Co-existence of Different Synchronization Types in Fractional-order Discrete-time Chaotic Systems with Non–identical Dimensions and Orders

This paper is concerned with the co-existence of different synchronization types for fractional-order discrete-time chaotic systems with different dimensions. In particular, we show that through appropriate nonlinear control, projective synchronization (PS), full state hybrid projective synchronization (FSHPS), and generalized synchronization (GS) can be achieved simultaneously. A second nonlinear control scheme is developed whereby inverse full state hybrid projective synchronization (IFSHPS) and inverse generalized synchronization (IGS) are shown to co-exist. Numerical examples are presented to confirm the findings.