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Singular perturbation analysis in a coupled Chua's circuit with diffusion.

Zhengkang Li1, Xingbo Liu2

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Summary
This summary is machine-generated.

This study proves traveling wave solutions exist in Chua's circuit systems, revealing a heteroclinic cycle with identical wave speeds. This cycle generates complex hyperchaotic behavior.

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Area of Science:

  • Nonlinear Dynamics
  • Circuit Theory
  • Chaos Theory

Background:

  • Chua's circuit is a fundamental nonlinear electronic circuit.
  • Coupled arrays of Chua's circuit exhibit complex dynamics.
  • Traveling wave solutions are crucial for understanding wave propagation in such systems.

Purpose of the Study:

  • To investigate traveling wave solutions in singularly perturbed systems derived from coupled Chua's circuit arrays.
  • To analyze the existence and properties of heteroclinic cycles.
  • To characterize the chaotic behavior associated with these solutions.

Main Methods:

  • Geometric singular perturbation theory.
  • Invariant manifold theory.
  • Analysis of heteroclinic cycles.

Main Results:

  • Existence of a heteroclinic cycle with traveling front and back waves sharing the same speed.
  • Derivation of the expression for the wave speed.
  • Identification of hyperchaos induced by the heteroclinic cycle.

Conclusions:

  • The study confirms the existence of specific traveling wave solutions in coupled Chua's circuit systems.
  • The identified heteroclinic cycle is a source of complex, hyperchaotic dynamics.
  • This research provides insights into the wave propagation and chaotic phenomena in nonlinear circuits.