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Noise induced complexity: from subthreshold oscillations to spiking in coupled excitable systems
M A Zaks1, X Sailer, L Schimansky-Geier
1Institut für Physik, Humboldt-Universität zu Berlin, Newtonstrasse 15, D-12489 Berlin, Germany. zaks@physik.hu-berlin.de
Chaos (Woodbury, N.Y.)
|July 23, 2005
Summary
Noise can surprisingly drive coupled FitzHugh-Nagumo oscillators from steady states to oscillations and chaos. Increasing noise levels reveal complex collective dynamics, transitioning back to equilibrium in this study of stochastic systems.
Area of Science:
- Computational Neuroscience
- Nonlinear Dynamics
- Statistical Physics
Background:
- Excitable elements, like FitzHugh-Nagumo oscillators, are fundamental in modeling biological systems.
- Understanding the collective behavior of coupled oscillators under noise is crucial for complex system dynamics.
Purpose of the Study:
- To investigate the impact of Gaussian noise on the collective dynamics of globally coupled FitzHugh-Nagumo oscillators.
- To characterize noise-induced transitions in the mean-field behavior of the ensemble.
Main Methods:
- Simulations of Langevin dynamics for N coupled FitzHugh-Nagumo oscillators.
- Analysis of the ensemble's mean-field behavior.
- Derivation of a cumulant expansion for mean-field fluctuations in the thermodynamic limit (N→∞).
- Bifurcation analysis in Gaussian approximation.
Main Results:
- Increasing noise induces transitions from steady equilibrium to global oscillations, and then back to equilibrium.
- Diverse collective dynamics, including subthreshold oscillations, large-amplitude oscillations, and chaos, are observed during these transitions.
- Theoretical analysis in the thermodynamic limit qualitatively agrees with simulation results.
Conclusions:
- Noise plays a critical role in shaping the collective dynamics of excitable ensembles.
- The study provides a theoretical framework for understanding noise-induced transitions and complex behaviors in coupled oscillator systems.