Composition Methods for the Simulation of Arrays of Chua's Circuits 1 Composition Methods for the Simulation of Arrays of Chua's Circuits

1 This report is available by anonymous ftp from ftp.esat.kuleuven.ac.be in the directory pub/SISTA/moreau/reports/. The missing gures, which have been excluded because they are diicult to print, are available separately in the le chua gures.ps. Abstract Composition methods are methods for the integration of ordinary differential equations arising from diierential 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 eld of the array of Chua's circuits into its linear part and its nonlinear part. We then solve the elementary diierential equation for each part separatelyywhich is easy since the equations for the nonlinear part are all decoupleddand 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: xed time-step explicit Euler and adaptive fourth-order Runge-Kutta.