Analytical Approach to Noise Effects on Synchronization in a System of Coupled Excitable Elements

@inproceedings{Okumura2010AnalyticalAT,
  title={Analytical Approach to Noise Effects on Synchronization in a System of Coupled Excitable Elements},
  author={Keiji Okumura and Masatoshi Shiino},
  booktitle={ICONIP},
  year={2010}
}
We report relationships between the effects of noise and applied constant currents on the behavior of a system of excitable elements. The analytical approach based on the nonlinear Fokker-Planck equation of a mean-field model allows us to study the effects of noise without approximations only by dealing with deterministic nonlinear dynamics . We find the similarity, with respect to the occurrence of oscillations involving subcritical Hopf bifurcations, between the systems of an excitable… 
1 Citations

IEICE Proceeding Series

It is shown that photonic reservoirs can achieve an even better performance on a benchmark isolated digit recognition task, if the interconnection delay is optimized and the phase can be controlled.

References

SHOWING 1-8 OF 8 REFERENCES

Chaos-nonchaos phase transitions induced by external noise in ensembles of nonlinearly coupled oscillators.

  • M. ShiinoK. Yoshida
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2001
An H theorem is proposed for the nonlinear Fokker-Planck equation to ensure stability of the Gaussian type solution that is approached for large times and is found to occur as the noise level is changed.

Noise induced complexity: from subthreshold oscillations to spiking in coupled excitable systems.

In simulations of the Langevin dynamics, the collective behavior of the ensemble is characterized in terms of its mean field and it is shown that with the increase of noise the mean field displays a transition from a steady equilibrium to global oscillations and then, for sufficiently large noise, back to another equilibrium.

Noise-induced synchronous neuronal oscillations.

  • KurrerSchulten
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1995
Analytical calculations and computer simulations show that coupled excitable systems can undergo two different phase transitions from synchronous to asynchronous firing behavior, one of the transitions is akin to the synchronization transitions in coupled oscillator systems, while the second transition can only be found in coupled excited systems.

Coherence resonance and noise-induced synchronization in globally coupled Hodgkin-Huxley neurons.

  • Y. WangD. ChikZ. D. Wang
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 2000
The coherence resonance (CR) of globally coupled Hodgkin-Huxley neurons is studied and a bell-shaped curve is found for the peak height of power spectra of the spike train, being significantly different from a monotonic behavior for the single neuron.

Analysis of globally connected active rotators with excitatory and inhibitory connections using the Fokker-Planck equation.

  • T. KanamaruM. Sekine
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2003
The globally connected active rotators with excitatory and inhibitory connections are analyzed using the nonlinear Fokker-Planck equation and the relationship of the model to the biological data is discussed.

Nonlinear Fokker-Planck Equations