# Synchronization of Chaotic Oscillators With Partial Linear Feedback Control

## TL;DR

This paper introduces a new method for synchronizing chaotic oscillators using partial linear feedback, analyzing them as multi-mode linear systems and ensuring stability through classical control techniques, with applications in cryptography.

## Contribution

It proposes a novel synchronization approach for chaotic oscillators with partial feedback, combining multi-mode analysis and root-locus design for stability.

## Key findings

- Successful numerical simulations demonstrating synchronization
- Experimental validation with electronic chaotic circuits
- Potential application in secure communication systems

## Abstract

We present a methodology for synchronization of chaotic oscillators with linear feedback control. The proposed method is based on analyzing the chaotic oscillator as a multi-mode linear system and deriving sufficient conditions for asymptotic stability. The oscillators are synchronized in a master-slave configuration, wherein a subset of the state variables for implementing the feedback control, enabling applications in cryptography for message encryption using the unused chaotic state variables. Controller stability is ensured through conventional root-locus technique for designing appropriate loop gain. We validate the methodology presented here with numerical simulations and experimental results obtained using an operational amplifier (op-amp) based electronic chaotic oscillator circuit.