Numerical and analytical study of the synchronization of different nonlinear systems with potential \(\Phi ^{8}\)
摘要
In this paper the synchronization of van der Pol-Duffing and Duffing systems, with a four-well potential, is studied by using the classical master–slave configuration. It is established the requirements the potential needs to satisfy to get the configurations of single-well, double-well, triple-well or quadruple-well potential. Synchronization with gyroscopic and combined elastic-gyroscopic couplings is analyzed for this system, obtaining an analytic solution for the slave system using perturbation theory in the limit of strong coupling. The approximate solutions are used to analyze the vertical shift phenomenon between the solutions provided by the master and slave systems founded in this and previous numerical analysis. We found that this phenomenon is a problem of asymptotic behavior of the numerical solution that can be suppressed by considering times large enough.