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

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.