Dynamics of two coupled van der Pol oscillators

Abstract

A system of two coupled van der Pol oscillators showing multistable behavior for some control parameter ranges is studied. When several attractors coexist a rich fractal structure is found both on the border between basins and in extended zones of the phase space. In such zones strong mixing and self-similar structure of basins are manifest. A relationship is observed between the appearance of symmetric attractors and the fractal properties of the attraction basins. First return maps, Poincar\'e sections, and probability distribution functions have been computed for the model equations, indicating that the complex dynamics found in the system can be understood in terms of more simple discrete transformations related to the logistic map. A combined master-slave system based on the coupled oscillators studied is found to enter a chaotic synchronization regime for some values of the control parameters. The practical implications of the observed phenomena are discussed.