Nonlinear dynamics and strange attractors in the biological system

This paper deals with the nonlinear dynamics of the biological system modeled by the multi-limit cycles Van der Pol oscillator. Both the autonomous and non-autonomous cases are considered using the analytical and numerical methods. In the autonomous state, the model displays phenomenon of birhythmicity while the harmonic oscillations with their corresponding stability boundaries are tackled in the non-autonomous case. Conditions under which superharmonic, subharmonic and chaotic oscillations occur in the model are also investigated. The analytical results are validated and supplemented by the results of numerical simulations.