excitabledynamics

Excitabledynamics refers to the study of how systems that are excitable respond to stimuli with large transient events, followed by refractory periods. It encompasses neurons, cardiac tissue, and certain chemical and ecological systems. The field analyzes how thresholds, timing, and network structure shape spike initiation and wave propagation.

Core concepts include excitability (a system's ability to respond dramatically to stimuli), the existence of a threshold, an all-or-none spike, and refractory dynamics that prevent immediate re-excitation. Other features include recovery variables, afterhyperpolarization, and the role of slow variables in governing timing.

Mathematical models used to analyze excitabledynamics include the FitzHugh-Nagumo and Hodgkin-Huxley models for neural excitability, Morris-Lecar, and cardiac models like Luo-Rudy. These models split dynamics into fast variables (e.g., membrane potential) and slow recovery variables, enabling bifurcation and phase-plane analyses.

Dynamics in spatially extended media lead to wave propagation, including traveling pulses, spiral waves, and reentrant activity. Pattern formation and spatiotemporal chaos can arise from interactions of excitable elements, diffusion, and heterogeneous properties, making excitabledynamics relevant to both normal function and pathological states.

Applications span neuroscience, cardiology, and engineered systems. Insights inform understanding of information processing, arrhythmias, and chemical reaction-diffusion phenomena. The field integrates theory, simulation, and experimentation to characterize how excitability governs temporal and spatial patterns in complex systems.