Multirhythmicity generated by slow variable diffusion in a ring of relaxation oscillators and noise-induced abnormal...

Area of Science:

• Nonlinear Dynamics
• Complex Systems
• Electronic Circuits

Background:

• Electronic relaxation oscillators exhibit complex behaviors, including limit cycles arising from nonlinear characteristics.
• Coupling multiple oscillators can lead to emergent dynamics not present in isolated units.

Purpose of the Study:

• Investigate the deterministic and noise-dependent dynamics of three Ohmically coupled electronic relaxation oscillators.
• Analyze the phase diagram and identify parameter regions leading to specific limit cycles, including dynamic traps.
• Examine the impact of noise on interspike interval (ISI) distributions in different dynamical regimes.

Main Methods:

• Numerical simulations of a system of three coupled ordinary differential equations representing electronic relaxation oscillators.
• Calculation of the phase diagram for the coupled system with detuning.
• Analysis of interspike interval (ISI) distributions as a function of coupling strength and noise levels.

Main Results:

• Identified two key parameter areas: near homogeneous and inhomogeneous stable steady states.
• Observed asymmetric limit cycles, termed 'dynamic traps,' where some oscillators exhibit reduced activity.
• Found extremely polymodal ISI distributions near homogeneous states, indicating high variability, even with dominant in-phase oscillations.
• Demonstrated that nontrivial periodic attractors near inhomogeneous states require low noise levels, resulting in near-unimodal ISI distributions.

Conclusions:

• The coupling and detuning of electronic relaxation oscillators lead to complex dynamics, including dynamic traps.
• Noise plays a critical role in shaping the interspike interval variability, with significantly different outcomes near homogeneous and inhomogeneous steady states.
• Understanding these dynamics is crucial for designing and controlling coupled oscillator systems.