Interpolating between bumps and chimeras

Area of Science:

• Computational neuroscience
• Complex systems dynamics
• Nonlinear dynamics

Background:

• Neuronal 'bumps' and oscillator 'chimeras' are distinct network patterns with similar appearances.
• These patterns are often studied in isolation within their respective network types.
• Conflation of these patterns can arise due to superficial similarities and co-occurrence in similar network architectures.

Purpose of the Study:

• To numerically investigate a hybrid system interpolating between bump and chimera networks.
• To analyze the behavior of this hybrid system using theoretical frameworks.
• To clarify the distinct characteristics and parameter dependencies of bumps and chimeras within a unified model.

Main Methods:

• Development of a hybrid network model linearly interpolating between theta neuron and phase oscillator networks.
• Application of the Ott/Antonsen ansatz to derive network equations in the infinite oscillator limit.
• Bifurcation analysis to systematically explore the parameter space of the hybrid system.

Main Results:

• Neither the bump nor the chimera pattern is universally present across the entire parameter range.
• The hybrid system exhibits a rich variety of emergent states beyond bumps and chimeras.
• Observed states include spatiotemporal chaos, traveling waves, and modulated traveling waves.

Conclusions:

• The distinct network patterns (bumps and chimeras) have specific parameter regimes and do not universally coexist.
• Hybrid systems offer a framework to explore transitions between different dynamic states in neural and oscillator networks.
• Understanding these transitions is crucial for deciphering complex collective behaviors in diverse dynamical systems.