# Co-coupled synchronization of fractional-order unified chaotic systems

## TL;DR

This paper investigates co-coupled synchronization of fractional-order chaotic systems with different initial conditions, deriving a synchronization theorem and confirming coupling coefficient ranges through simulations, demonstrating effectiveness.

## Contribution

It introduces a new synchronization theorem for fractional-order chaotic systems and confirms coupling coefficient ranges using Lyapunov stability and Gerschgorin theorem.

## Key findings

- Synchronization achieved between fractional-order chaotic systems.
- Theoretical coupling coefficient ranges confirmed.
- Simulation results validate the synchronization method.

## Abstract

Synchronization of fractional-order chaotic systems is a hot topic in the field of nonlinear study. The co-coupled synchronization between two fractional-order chaotic systems with different initial conditions is investigated in this paper. Based on Lyapunov stability principle and Gerschgorin theorem, the co-coupled synchronization theorem of fractional-order chaotic systems is deduced, and the range of coupling coefficients is confirmed for synchronization of fractional-order unified chaotic systems. By building up the synchronization simulation model on Simulink, the co-coupled synchronization between two fractional-order unified chaotic systems with different initial value is carried out, and the synchronization performances are analyzed, and the simulation results show that this synchronization method is effective.

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Source: https://tomesphere.com/paper/0909.2410