Anomalous relaxation oscillations due to dynamical traps

We consider relaxation oscillation governed by the coupled equations αẋ=(x−x0)1+pQ(x,y), ẏ=P(x,y), where α is a small parameter (α⪡1), p and x0 are given constants, and Q,P are nonlinear functions. We investigate the relaxation oscillations in the system and it is shown that their limit cycle exhibits anomalous properties. It is shown that small fluctuations affect the system behavior and its motion near the line x=x0 can give rise to the strong chaotic behavior of the system. Lyapunov exponents are calculated for the given system and fractal dimensions are determined for the chaotic attractors of the system.