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Activation process in excitable systems with multiple noise sources: One and two interacting units.

Igor Franović1, Kristina Todorović2, Matjaž Perc3,4

  • 1Scientific Computing Laboratory, Institute of Physics, University of Belgrade, P. O. Box 68, 11080 Beograd-Zemun, Serbia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary

This study investigates how two noise sources impact excitable systems, like the Fitzhugh-Nagumo equations. We identified key activation paths and analyzed how noise and interactions alter system dynamics and transitions.

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Area of Science:

  • Computational neuroscience
  • Nonlinear dynamics
  • Stochastic processes

Background:

  • Excitable systems, crucial in biology and physics, are often influenced by multiple noise sources.
  • Understanding noise coaction is vital for predicting system behavior and transitions.
  • The Fitzhugh-Nagumo model provides a simplified yet powerful framework for studying excitable dynamics.

Purpose of the Study:

  • To analyze the impact of two distinct noise sources on the activation pathways of single and coupled excitable units.
  • To determine the most probable activation paths and understand how noise influences stochastic trajectories.
  • To investigate the role of interaction linearity/nonlinearity in shaping activation dynamics.

Main Methods:

  • Mathematical modeling using the Fitzhugh-Nagumo equations.
  • Introduction of specific boundary conditions for Class II excitable units.
  • Analysis of stochastic trajectories and statistical features of the activation process.
  • Investigation of noise effects on coupled unit interactions.

Main Results:

  • Identified most probable activation paths for stochastic trajectories in excitable systems.
  • Demonstrated how two distinct noise sources collectively influence activation processes.
  • Showcased the modification of statistical features due to linear and nonlinear interactions.
  • Observed universal properties related to stochastic bifurcations.

Conclusions:

  • The coaction of noise sources significantly shapes activation pathways and dynamics in excitable systems.
  • Interaction type (linear vs. nonlinear) critically modulates the effects of noise.
  • The study provides insights into stochastic bifurcations and transitions in excitable media.