Analysis of Chua Circuit Dynamics (Tentative Title ) (Authors: Mishty Ray, Amol Amodkar and Harman Kaur)


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.


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Chua circuit basics

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

Block diagram for Chua's circuit

Here \(L\) is the inductor, \(\ C_1\ \) and \( \ C_2\ \) are capacitors, \( \ N_R \ \) is the non-linear source of current and \( R \) is a variable resistor. In the actual circuit, we replace the inductor and non-linear component with op-amps, capacitors and resistors as shown below.