Transformation of Master-Slave Systems with Harmonic Terms for Improved Stability in Numerical Continuation
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Proceedings |
| Conference | 15th Chaotic Modeling and Simulation International Conference |
| MU Faculty or unit | |
| Citation | |
| web | https://doi.org/10.1007/978-3-031-27082-6_7 |
| Doi | http://dx.doi.org/10.1007/978-3-031-27082-6_7 |
| 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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