Publication details

Transformation of Master-Slave Systems with Harmonic Terms for Improved Stability in Numerical Continuation



Year of publication 2023
Type Article in Proceedings
Conference 15th Chaotic Modeling and Simulation International Conference
MU Faculty or unit

Faculty of Science

Keywords Master-slave systems; Harmonic coupling terms; Arnold tongues; Synchronization; Numerical continuation
Description Nonlinear problems with forced oscillations occur in many applications in physics, neuroscience, epidemiology, or physiology. Forced oscillations are usually modeled as non-autonomous master-slave systems with harmonic driving. The aim of this work is to provide a transformation suitable for analyzing such systems via standard numerical continuation packages such as MATCONT and AUTO. We transform the original system into a structurally stable generalized system by replacing each harmonic term in the original system by a supercritical Hopf bifurcation normal form subsystem. Our method is general; being applicable to an important class of nonlinear equations in which the driving or coupling occurs via harmonic terms involving phases. Here we apply it to analyze the dynamics of a driven single Josephson junction, shunted by an inductor-resistor-capacitor resonant circuit.
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