Spiking at the edge: Excitability at interfaces in reaction-diffusion systems.

Area of Science:

• Nonlinear dynamics
• Reaction-diffusion systems
• Complex systems

Background:

• Excitable media typically require coexisting amplification and suppression for spiking.
• Spiking in traditional models arises from local bistabilities, demanding fine-tuned parameters.
• Natural and engineered systems often exhibit spatial segregation of these forces.

Purpose of the Study:

• To investigate how spatial segregation of forces, specifically at boundaries, can lead to spiking.
• To demonstrate that spiking can emerge at interfaces even when local conditions do not support it.
• To provide a theoretical framework for understanding edge spiking in reaction-diffusion systems.

Main Methods:

• Analytical derivation of a spiking phase diagram.
• Analysis of reaction-diffusion models with segregated amplification and suppression.
• Exploration of the role of diffusion and system size.

Main Results:

• Weak diffusion at boundaries can induce spiking in non-excitable media.
• Edge spiking arises from a global bistability, independent of local spiking conditions.
• A phase diagram is derived based on system size/diffusion length and amplification/suppression ratios.

Conclusions:

• Boundaries can act as generators of spiking activity in excitable media.
• Edge spiking provides a mechanism for interfacial excitations in diverse systems.
• Findings have implications for bioelectricity, chemical reactions, and neuromorphic computation.