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Volume 3, Number 3, 2013, Pages 213-237                                                                DOI:10.11948/2013016
Traveling Wave Solutions In Coupled Chua'S Circuits,Part I: Periodic Solutions
Shui-Nee Chow,Ming Jiang,Xiaobiao Lin
Keywords:Chua's circuits;singular perturbations
      We study a singularly perturbed system of partial di erential equations that models a one-dimensional array of coupled Chua's circuits. The PDE system is a natural generalization to the FitzHugh-Nagumo equation. In part I of the paper, we show that similar to the FitzHugh-Nagumo equation, the system has periodic traveling wave solutions formed alternatively by fast and slow flows. First, asymptotic method is used on the singular limit of the fast/slow systems to construct a formal periodic solution. Then, dynamical systems method is used to obtain an exact solution near the formal periodic soluion. In part II, we show that the system can have more complicated periodic and chaotic traveling wave solutions that do not exist in the FitzHugh-Nagumos equation.
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