# Abstract

Chua’s circuit is a common model dynamical system that exhibits chaotic behaviour for a certain set of parameters. We worked with the dimensionless formulation of a slightly modified version of the Chua equations with only one variable parameter, $$R$$ (resistance). We analyzed the stability of the system and explicitly computed stable and unstable points for illustration at $$R=2100$$ ohms. We observed and demonstrated period-doubling bifurcations in the $$x$$ component which occurred on varying the parameter $$R$$. We moved on to analyze the transition to chaos and observed multiple attractors at $$R=1800$$ ohms. Finally for data assimilation, we used synchronization and Ensemble Kalman Filter(EnK) and then compared the error in both. EnK fared better for a given timestep.

# Introduction

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# Chua circuit basics

The Chua circuit is a basic LCR circuit that exhibits chaotic behaviour.