Anti-phase solutions in relaxation oscillators coupled through excitatory interactions

Area of Science:

• Computational Neuroscience
• Systems Neuroscience
• Theoretical Neuroscience

Background:

• Relaxation oscillators are fundamental to understanding neural dynamics.
• Interactions via excitatory chemical synapses with sharp thresholds are common in neural circuits.
• Both in-phase and anti-phase synchronization patterns can emerge from coupled oscillator systems.

Purpose of the Study:

• To investigate the mechanism behind stable anti-phase solutions in interacting relaxation oscillators.
• To analyze the role of excitatory synaptic input in generating anti-phase synchronization.
• To validate the findings in abstract models with widely used descriptions of bursting neurons.

Main Methods:

• Analysis of relaxation oscillators coupled through excitatory chemical synapses with sharp thresholds.
• Development of an abstract model to elucidate the
• virtual delay
• mechanism.
• Application and validation of the abstract model to specific neural models of bursting neurons.

Main Results:

• Demonstration of stable anti-phase solutions in addition to in-phase solutions for interacting relaxation oscillators.
• Identification of a
• virtual delay
• mechanism, where excitatory input slows the receiving oscillator.
• Confirmation that this virtual delay mechanism is applicable to common bursting neuron models.

Conclusions:

• Excitatory chemical synapses with sharp thresholds can induce stable anti-phase synchronization in neural networks.
• The
• virtual delay
• induced by excitatory input is a key mechanism for anti-phase firing.
• This finding provides a mechanistic understanding of anti-phase dynamics in biologically relevant neural models.