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Area of Science:

  • Physics
  • Dynamical Systems
  • Neuroscience

Background:

  • Chimera states, a phenomenon where coherence and incoherence coexist in identical coupled oscillators, have been observed in various systems.
  • The emergence of mixed-mode chimera states, involving both rotating and quiescent oscillators, is a novel observation in coupled pendula networks.
  • These mixed-mode states bear resemblance to bump states observed in neuroscience models of working memory.

Purpose of the Study:

  • To investigate the emergence and characteristics of peculiar chimera states in networks of identical pendula with global phase-lagged coupling.
  • To analyze the coexistence of rotating and quiescent modes within these chimera states.
  • To explore the potential connection between these mixed-mode chimera states and neural network dynamics, specifically working memory.

Main Methods:

  • Simulations of a network of N=100 coupled pendula to observe chimera states.
  • Detailed analysis of the minimal non-trivial case with N=3 coupled pendula.
  • Identification of parameter regions for different system behaviors, including mixed-mode chimeras, classical chimeras, synchronous rotation, and quiescent states.
  • Investigation of network multistability using basins of attraction analysis.

Main Results:

  • The emergence of peculiar chimera states with both rotating (non-zero average frequency) and quiescent (zero average frequency) pendula was confirmed.
  • Five characteristic types of system behavior were identified: two types of mixed-mode chimeras (one and two rotating pendula), classical weak chimera, synchronous rotation, and a quiescent state.
  • The network dynamics were found to be multistable, with up to four different states coexisting within the system's phase space.
  • Basins of attraction analysis demonstrated the robust coexistence of these diverse states.

Conclusions:

  • Mixed-mode chimera states represent a significant finding in the study of coupled oscillator networks.
  • These states provide a potential dynamical systems analogue for neural bump states underlying working memory.
  • The identified chimera states are robust and can generically describe complex dynamics in various pendula-like systems found in nature.