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Noisy FitzHugh-Nagumo model: from single elements to globally coupled networks
J A Acebrón1, A R Bulsara, W-J Rappel
1Department of Physics, University of California-San Diego, La Jolla, CA 92093, USA.
Summary
We analyzed the noisy FitzHugh-Nagumo model, finding that coupled neural networks exhibit Hopf bifurcations absent in single elements. External driving forces induce resonance in these networks.
Area of Science:
- Computational Neuroscience
- Theoretical Physics
- Mathematical Biology
Background:
- The FitzHugh-Nagumo model simulates excitable systems, crucial for understanding neural dynamics.
- Analyzing noise effects and network coupling is essential for realistic neural modeling.
Purpose of the Study:
- To investigate the dynamics of the noisy FitzHugh-Nagumo model for single elements and globally coupled networks.
- To develop efficient numerical methods for solving the derived Fokker-Planck equation, particularly at high noise levels.
- To explore bifurcations and resonance phenomena in these systems.
Main Methods:
- Derivation of the Fokker-Planck equation for single and coupled FitzHugh-Nagumo elements.
- Development of an efficient numerical solver for the Fokker-Planck equation, handling large noise intensities.
- Analytical investigation of resonance phenomena using timescale separation.
Main Results:
- The coupled network exhibits a Hopf bifurcation with increasing coupling strength, unlike the single element.
- An external sinusoidal driving force induces classical resonance when its frequency aligns with the system's natural frequency.
- The numerical method proves efficient, especially for high noise levels.
Conclusions:
- Network coupling introduces distinct dynamical behaviors, such as Hopf bifurcations, not present in isolated elements.
- Resonance phenomena are significant in driven excitable networks and can be analyzed by exploiting timescale differences.
- The developed numerical approach enhances the study of noisy nonlinear dynamical systems.