Dynamics of a stochastic excitable system with slowly adapting feedback

Area of Science:

• Physics
• Nonlinear Dynamics
• Computational Neuroscience

Background:

• Excitable systems with nonlinear feedback and noise exhibit complex dynamics.
• Understanding these dynamics is crucial for modeling biological systems like neurons.

Purpose of the Study:

• To investigate the dynamical regimes of an excitable active rotator with slow adaptation and noise.
• To analyze transitions between spiking, oscillatory, and bursting behaviors.
• To explore control mechanisms for coherence resonance and stochastic bursting.

Main Methods:

• Utilized a multiple timescale approach combining adiabatic elimination and averaging.
• Employed stochastic averaging via a stationary Fokker-Planck equation.
• Performed numerical bifurcation analysis on a reduced slow system.

Main Results:

• Identified parameter regions for noise-induced spiking, noise-perturbed oscillations, and stochastic bursting.
• Demonstrated noise-induced switching between stationary and oscillatory regimes, leading to stochastic bursting.
• Showcased methods to enhance/suppress coherence resonance and control bursting features.

Conclusions:

• The model serves as a paradigm for neurons with slow recovery or excitable systems with nonlinear control.
• Noise and adaptation play critical roles in shaping the system's complex dynamics.
• The multiple timescale approach effectively analyzes and predicts system behavior across different regimes.