Abstract
We report an investigation of the oscillation death (OD) of a parametrically excited coupled van der Pol–Mathieu (vdPM) system. The system can be considered as a pair of harmonically forced van der Pol oscillators under a double-well potential. The two oscillators are coupled with a cubic nonlinearity. We have shown that the system arrives at an OD regime when coupling strength crosses a threshold value at which the system undergoes saddle-node bifurcation and two limit cycles coalesce onto a fixed point of the system. We have further shown that this nonautonomous system possesses a centre manifold corresponding to the OD regime.
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BORA, M.P., SARMAH, D. Oscillation death in a coupled van der Pol–Mathieu system. Pramana - J Phys 81, 677–690 (2013). https://doi.org/10.1007/s12043-013-0595-3
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DOI: https://doi.org/10.1007/s12043-013-0595-3