The reliability of the stochastic active rotator

Area of Science:

• Computational Neuroscience
• Dynamical Systems Theory
• Stochastic Processes

Background:

• Excitable-oscillating systems are fundamental in neuroscience for understanding neuronal firing.
• The reliability of neuronal responses to noisy inputs is crucial for information processing.
• Previous models often simplified neuronal dynamics, limiting insights into reliability mechanisms.

Purpose of the Study:

• To investigate the reliability of firing in excitable-oscillating systems using a neuronal model.
• To analyze the response of the active rotator model to white Gaussian noise.
• To introduce and utilize a stochastic return map to characterize model behavior.

Main Methods:

• Simulated the active rotator model, a neuronal model on the unit circle.
• Applied white Gaussian noise as input to the active rotator.
• Developed and analyzed a stochastic return map to identify fixed points and dynamics.

Main Results:

• The stochastic return map revealed one stable and one unstable fixed point.
• Almost all initial conditions converged to the stable fixed point, indicating unique asymptotic responses.
• The active rotator demonstrated reliable responses to identical, repeated noise stimuli after a transient period.

Conclusions:

• The active rotator model exhibits reliable firing due to its nonuniform motion on the unit circle.
• This reliability suggests that neuronal models with phase dynamics similar to the active rotator may share these properties.
• The findings provide a framework for understanding reliable neuronal signaling in the presence of noise.