A new fractional order chaotic dynamical system and its synchronization using optimal control

TL;DR

This paper introduces a new three-dimensional fractional order chaotic system, analyzes its stability, and develops optimal control methods for chaos synchronization, supported by numerical simulations.

Contribution

The paper presents a novel fractional order chaotic system and proposes an optimal control strategy for its synchronization, extending existing chaos control techniques.

Findings

Stability conditions for various fractional orders established

Numerical simulations confirm chaotic behavior and control effectiveness

Optimal control successfully synchronizes the new chaotic system

Abstract

In this work, we introduce a new three-dimensional chaotic differential dynamical system. We find equilibrium points of this system and provide the stability conditions for various fractional orders. Numerical simulations will be used to investigate the chaos in the proposed system. A simple linear control will be used to control the chaotic oscillations. Further, we propose an optimal control which is based on the fractional order of the system and use it to synchronize new chaotic system.