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Updated: Jun 22, 2026
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Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond
Published on: June 24, 2015
Stationary pattern formation in a discrete excitable system with strong inhibitory coupling
Naoko Kurata1, Hiroyuki Kitahata, Hitoshi Mahara
1Graduate School of Science, Chiba University, Chiba 263-8522, Japan.
Summary
This study explores coupled excitable elements using FitzHugh-Nagumo equations. Nontrivial stable states emerge based on coupling strengths, influencing pattern formation in arrays.
Area of Science:
- Computational neuroscience
- Complex systems dynamics
Background:
- The FitzHugh-Nagumo model is a simplified mathematical model of excitable systems, often used to study phenomena like nerve impulse propagation.
- Understanding the behavior of coupled excitable elements is crucial for modeling complex biological and physical systems.
Purpose of the Study:
- To investigate the emergence and stability of states in a discrete model of coupled excitable elements.
- To analyze stationary pattern formation in one-dimensional and two-dimensional arrays based on FitzHugh-Nagumo dynamics.
Main Methods:
- Utilizing a discrete model based on monostable FitzHugh-Nagumo equations.
- Analyzing a system with a weakly coupled activator and a strongly coupled inhibitor.
- Examining the stability of trivial and nontrivial states for two-coupled elements.
- Investigating pattern formation in one-dimensional arrays and two-dimensional lattices.
Main Results:
- The trivial state is always stable in a two-coupled system.
- Nontrivial stable states appear and depend on specific coupling strengths.
- In a one-dimensional array, only elements near the initial condition maintain nontrivial states.
- Analytical results from the two-coupled system inform pattern formation discussions.
Conclusions:
- Coupling strengths critically determine the stability and emergence of nontrivial states in discrete excitable systems.
- Stationary patterns in arrays are influenced by local initial conditions and coupling parameters.
- The study provides insights into pattern formation mechanisms in spatially extended excitable media.
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