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Area of Science:

  • Physics
  • Computational Neuroscience
  • Complex Systems

Background:

  • Excitable systems are crucial for modeling natural phenomena, including neuronal activity.
  • Colored noise, with its temporal correlations, complicates analytical studies of these systems.
  • Existing methods struggle to provide exact solutions for systems driven by correlated noise.

Purpose of the Study:

  • To present a general method for reducing colored noise-driven excitable systems to tractable white-noise systems.
  • To develop an analytical framework for understanding the linear response of neuronal models under colored noise.
  • To enable the characterization of excitable units and network dynamics.

Main Methods:

  • Developed a general reduction technique transforming colored noise into effective, time-dependent boundary conditions for white-noise systems.
  • Applied the formalism to the leaky integrate-and-fire neuron model, a standard in computational neuroscience.
  • Derived a closed-form analytical expression for the system's linear response.

Main Results:

  • Successfully reduced a complex colored noise problem to a solvable white-noise framework.
  • Obtained an analytical expression for the linear response of the leaky integrate-and-fire neuron model.
  • The derived expression is valid for moderate frequencies, offering new analytical tractability.

Conclusions:

  • The developed method provides a powerful tool for analyzing excitable systems driven by colored noise.
  • The analytical results facilitate the characterization of individual excitable elements and emergent network behaviors.
  • This approach opens new avenues for studying phenomena in neuroscience and other fields involving correlated fluctuations.