Abstract
In this paper, we study stochasticity of nonlinear systems of Van der Pol-Mathieu type. At first, a sine circle map to the system is derived. Secondly, an approximate piecewise continuous map to the sine circle map is derived. Finally, we study stochasticity of the system based on Lyapunov exponents to mapped points of approximate piecewise continuous map and to oscillation of the original nonlinear systems. We show that if the oscillation of approximate piecewise continuous map is stochastic, that is Lyapunov exponent to the map is positive, then the oscillation of original system of Van der Pol-Mathieu type exhibits stochastic motion.
