Complex dynamics induced by multiple timescales in a Wilson-Cowan model with homeostatic plasticity

Area of Science:

• Computational Neuroscience
• Dynamical Systems Theory
• Mathematical Biology

Background:

• Homeostatic synaptic plasticity is vital for neural population stability, operating on slower timescales than neural activity.
• Neural mass models with homeostatic plasticity can exhibit complex dynamics, including mixed-mode oscillations (MMOs) and chaos.

Purpose of the Study:

• Investigate the dynamical mechanisms underlying complex behaviors in a single-node Wilson-Cowan model with homeostatic plasticity.
• Analyze the impact of three distinct timescales on neural population dynamics.

Main Methods:

• Studied a single-node Wilson-Cowan model incorporating homeostatic plasticity.
• Analyzed dynamics across two- and three-timescale frameworks.
• Investigated bifurcations of folded singularities and their role in transitions.

Main Results:

• Two-timescale analysis revealed canard-induced MMOs and period-doubling cascades linked to specific folded singularities.
• Three-timescale analysis demonstrated interactions between singularities, defining singular orbit structures.
• Identified degenerate folded points governing transitions between MMOs and relaxation oscillations.

Conclusions:

• The relative separation of timescales significantly influences complex dynamical behaviors in neural mass models.
• Folded singularities play a critical role in the transitions between different dynamic regimes.
• This work provides a comprehensive understanding of how synaptic weight dynamics contribute to neural population complexity.