TRAVELING WAVE SOLUTIONS IN COUPLED CHUA'S CIRCUITS, PART I: PERIODIC SOLUTIONS

Shui-Nee Chow; Ming Jiang; Xiaobiao Lin

doi:10.11948/2013016

2013 Volume 3 Issue 3

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Shui-Nee Chow, Ming Jiang, Xiaobiao Lin. TRAVELING WAVE SOLUTIONS IN COUPLED CHUA'S CIRCUITS, PART I: PERIODIC SOLUTIONS[J]. Journal of Applied Analysis & Computation, 2013, 3(3): 213-237. doi: 10.11948/2013016

Citation:

Shui-Nee Chow, Ming Jiang, Xiaobiao Lin. TRAVELING WAVE SOLUTIONS IN COUPLED CHUA'S CIRCUITS, PART I: PERIODIC SOLUTIONS[J]. Journal of Applied Analysis & Computation, 2013, 3(3): 213-237. doi: 10.11948/2013016

TRAVELING WAVE SOLUTIONS IN COUPLED CHUA'S CIRCUITS, PART I: PERIODIC SOLUTIONS

1 School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA;
2 Department of Mathematics, Augustana College, Rock Island, Illinois, 61201-2296, USA;
3 Department of Math. NC State University, Raleigh, NC, 27695-8205, USA

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Abstract

Abstract

We study a singularly perturbed system of partial differential 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.
- Chua's circuits /
- singular perturbations /
- traveling waves /
- periodic orbits /
- exponential dichotomy /
- Melnikov's method
MSC: 34C25;34C37;34E15;35B25;47N70

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