Composition Methods for the Simulation of Arrays of Chua’s Circuits

Composition methods are methods for the integration of ordinary differential equations arising from differential geometry, or more precisely, Lie algebra theory. We apply them here to the simulation of arrays of Chua’s circuits. In these methods, we split the vector field of the array of Chua’s circuits into its linear part and its nonlinear part. We then solve the elementary differential equation for each part separately — which is easy since the equations for the nonlinear part are all decoupled — and recombine these contributions into a sequence of compositions. This splitting gives rise to simple integration rules for arrays of Chua’s circuits, which we compare to more classical approaches: fixed time-step explicit Euler and adaptive fourth-order Runge–Kutta.