Control of multistability in ring circuits of oscillators

Area of Science:

• Computational Neuroscience
• Nonlinear Dynamics
• Systems Biology

Background:

• Biological central pattern generators (CPGs) exhibit multistability, generating diverse firing patterns.
• These patterns are characterized by specific phase relationships between neuronal elements.
• Transient perturbations can induce shifts between these stable firing patterns.

Purpose of the Study:

• To systematically determine optimal perturbation timing for inducing firing pattern shifts in ring circuits.
• To visualize the solution space and attractive basins of multistable ring circuits.
• To develop a predictive model for pattern transitions based on phase resetting.

Main Methods:

• Utilized phase-response curve (PRC) theory for perturbation timing.
• Employed a circuit emulator based on iterative mapping of uncoupled oscillator PRCs.
• Visualized solution space using relative phases of N-1 oscillators.
• Accounted for the effect of perturbations on two subsequent bursts for accurate basin mapping.

Main Results:

• Successfully visualized attractive basins for ring circuits of 2, 3, and 4 oscillators.
• Enabled accurate prediction of phase resetting required for pattern transitions.
• Identified optimal timing and synaptic characteristics for a 'switch signal' to induce desired phase resetting.

Conclusions:

• PRC-based methods provide a systematic approach to controlling multistable dynamics in CPGs.
• Accurate prediction and induction of pattern transitions are achievable through precise perturbation.
• This framework advances understanding and manipulation of complex neural circuit behavior.