# Suppression of Chaos in Mutually Coupled Synchronized Generalized Lorenz Systems

## TL;DR

This paper investigates how mutual nonlinear coupling in generalized Lorenz systems can suppress chaos while maintaining synchronization, with potential transitions to anti-synchronization demonstrated through various analytical measures.

## Contribution

It introduces a control method that suppresses chaos in coupled Lorenz systems without losing synchronization, expanding understanding of chaos control in nonlinear dynamics.

## Key findings

- Chaos suppression achieved via parameter control.
- Synchronization maintained during chaos suppression.
- Transition from synchronization to anti-synchronization demonstrated.

## Abstract

In this work, the dynamics of a system of mutually coupled Generalized Lorenz systems (GLS) is investigated. The state variables of two Lorenz oscillators are coupled mutually via non-linear controls and synchronization is achieved between the state variables. We find that by suitably controlling a parameter having a bearing on the coupling coefficient between the two Lorenz oscillators, the GLS, while preserving synchronization is rendered to a state wherein chaotic nature of state variables is suppressed and state variables exhibit oscillatory character. The suppression of chaos is verified by power spectra, permutation entropy and Lyapunov exponent calculations. When operated in chaotic domain, we show the possibility of transition from the state of synchronization to the state of anti-synchronization.

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Source: https://tomesphere.com/paper/1907.03469