Propagation failure in discrete bistable reaction-diffusion systems: theory and experiments.

Area of Science:

• Physics
• Nonlinear dynamics
• Complex systems

Background:

• Reaction-diffusion systems are fundamental models in various scientific fields.
• Understanding wave front propagation is crucial for phenomena like pattern formation and signal transmission.
• Bistable systems exhibit multiple stable states, leading to complex dynamics.

Purpose of the Study:

• To investigate wave front propagation failure in discrete bistable reaction-diffusion systems.
• To develop a theoretical framework accounting for dissipative effects.
• To derive an analytical expression for the critical coupling parameter governing front propagation.

Main Methods:

• Development of a theoretical approach incorporating dissipative effects.
• Derivation of an analytical expression for critical coupling based on nonlinearity threshold.
• Validation through numerical simulations.
• Experimental verification using an electrical diffusive lattice.

Main Results:

• An analytical expression for critical coupling was derived.
• The theoretical predictions accurately matched numerical simulation results.
• Experimental data confirmed the theoretical model and simulation findings.

Conclusions:

• Dissipative effects play a significant role in wave front propagation failure.
• The derived critical coupling parameter effectively predicts the onset of front propagation.
• The study provides a robust theoretical and experimental framework for bistable reaction-diffusion systems.