Periodic pulsatile stimulation of a nonlinear oscillator

Area of Science:

• Computational Neuroscience
• Nonlinear Dynamics
• Physics of Oscillators

Background:

• Integrate-and-fire oscillators are fundamental models in neuroscience and physics.
• Understanding their response to external periodic forcing is crucial for explaining complex rhythmic behaviors.
• Previous studies often focused on specific stimulation protocols, limiting the scope of observed phenomena.

Purpose of the Study:

• To investigate phase-locking phenomena in an integrate-and-fire oscillator under pulsatile periodic stimulation.
• To analyze how variations in stimulation period and intensity influence the oscillator's behavior.
• To explore the impact of different perturbative mechanisms on the system's dynamics, including potential bistability.

Main Methods:

• Derivation and analysis of phase transition curves using functional iteration.
• Modeling pulsatile periodic stimulation with controllable parameters (period and intensity).
• Reduction of the analysis to two-parameter families of discontinuous circle maps.

Main Results:

• Identified various phase-locked patterns between the oscillator's intrinsic rhythm and the forcing system.
• Demonstrated that different perturbative mechanisms lead to distinct dynamic behaviors.
• Observed bistability in the system under specific conditions.

Conclusions:

• The study reveals a rich variety of phase-locking behaviors in periodically stimulated integrate-and-fire oscillators.
• The choice of perturbative mechanism significantly impacts the system's dynamics and potential for bistability.
• The findings provide insights into the control of rhythmic systems through external periodic inputs.