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Nonlinear dynamics and strange attractors in the biological system. (English) Zbl 1138.37050

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

MSC:

37N25 Dynamical systems in biology
34C28 Complex behavior and chaotic systems of ordinary differential equations
92B05 General biology and biomathematics
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
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