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This study explores hybrid neural networks, distinguishing between neuronal "bumps" and oscillator "chimeras." The research reveals these patterns do not persist across all parameters, leading to diverse network behaviors.

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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.