WANG Wan-yong, CHEN Li-juan. Weak Resonant Double Hopf Bifurcation of n van der Pol Oscillators With Delay Coupling[J]. Applied Mathematics and Mechanics, 2013, 34(7): 764-770. doi: 10.3879/j.issn.1000-0887.2013.07.012
Citation: WANG Wan-yong, CHEN Li-juan. Weak Resonant Double Hopf Bifurcation of n van der Pol Oscillators With Delay Coupling[J]. Applied Mathematics and Mechanics, 2013, 34(7): 764-770. doi: 10.3879/j.issn.1000-0887.2013.07.012

Weak Resonant Double Hopf Bifurcation of n van der Pol Oscillators With Delay Coupling

doi: 10.3879/j.issn.1000-0887.2013.07.012
  • Received Date: 2013-04-07
  • Rev Recd Date: 2013-05-25
  • Publish Date: 2013-07-15
  • Weak resonant double Hopf bifurcation of nvan der Pol oscillators with delay coupling was investigated. With an extended method of multiple scales, the complex amplitude equations were obtained. With the complex amplitudes expressed in a polar form, the complex amplitude equations were reduced to a two dimensional real amplitude system. The equilibria and their stability of the real amplitud equations were studied, and the dynamics around 2∶5 resonant point unfolded and classified. Some interesting phenomena are found, such as amplitude death, periodic solution and bistability, etc. Validity of the analytical results is proved by their consistency with numerical simulations.
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