Hyperchaos in Wilson-Cowan oscillator circuits

Area of Science:

• Computational neuroscience
• Dynamical systems theory
• Neural network modeling

Background:

• The Wilson-Cowan equations model neural population activity, known to produce limit cycles and chaos in coupled systems.
• Previous work demonstrated chaos in two coupled Wilson-Cowan oscillators, particularly with specific inhibitory-excitatory coupling.

Purpose of the Study:

• To investigate the emergence of hyperchaos in larger networks of coupled Wilson-Cowan oscillators.
• To explore the relationship between network complexity and the degree of hyperchaos.
• To connect these findings to the unpredictability observed in human behaviors.

Main Methods:

• Simulating chains, grids, and sparse networks of Wilson-Cowan oscillators.
• Analyzing the dynamics of these networks, focusing on the number of positive Lyapunov exponents to quantify hyperchaos.
• Correlating network size and structure with the observed complexity.

Main Results:

• Networks of Wilson-Cowan oscillators generate hyperchaos.
• The complexity of hyperchaos, measured by the number of positive Lyapunov exponents, increases linearly with the number of oscillators.
• This linear increase in complexity suggests a scalable mechanism for generating unpredictable neural dynamics.

Conclusions:

• Coupled Wilson-Cowan equations can generate hyperchaos in complex network structures.
• The linear scaling of hyperchaos with network size provides a potential neural basis for the unpredictability in human behaviors.
• These findings have implications for understanding aging, brain injuries, autism, intelligence, and creativity.