© 2015 World Scientific Publishing Company. Synchronization is a common phenomenon whereby a dynamical system follows the pacemaker provided by an external forcing. Often, such systems have multiple synchronization modes, which are equivalent solutions. We investigate the specific case of two to one synchronization produced by the periodic forcing of a van der Pol oscillator where two possible modes, shifted by one period of the modulation, exist. By studying the flow and the local Lyapunov exponents along the orbit we give an explanation of the noise induced jumps observed in a stochastic forced oscillator. While this investigation gives results that are specific to this system, the framework presented is more general and can be applied to any system showing similar jumping dynamics.
Algar, S., Stemler, T., & De Saedeleer, B. (2015). Noise Induced Jumping Dynamics between Synchronized Modes. International Journal of Bifurcation and Chaos, 25(12), 1530034. https://doi.org/10.1142/S0218127415300347