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Area of Science:

  • Complex systems
  • Network science
  • Nonlinear dynamics

Background:

  • Synchronization phenomena are crucial in various complex systems.
  • Chimera states, a coexistence of order and disorder, are observed in coupled oscillator networks.
  • Interlayer coupling in multilayer and multiplex networks introduces unique dynamics.

Purpose of the Study:

  • To investigate synchronization patterns in multilayer and multiplex networks with randomly pinned interlayer interactions.
  • To analyze the emergence of explosive synchronization and chimera states under different network topologies.
  • To provide theoretical insights into the behavior of interconnected systems with elusive interlayer dynamics.

Main Methods:

  • Theoretical analysis using mean-field approximations.
  • Modeling of multilayer networks with all-to-all interlayer connections.
  • Modeling of multiplex networks with mirror node interconnections.

Main Results:

  • Multilayer networks with all-to-all coupling exhibit successive explosive synchronization, leading to chimera states.
  • Multiplex networks with mirror node coupling show concurrent explosive transitions.
  • Mean-field analysis confirms the occurrence of both explosive synchronization and chimera states.

Conclusions:

  • Network topology significantly influences synchronization dynamics and the emergence of complex states.
  • Random pinning in interlayer interactions presents challenges and unique behaviors in interconnected systems.
  • Findings have implications for understanding real-world coupled systems where interlayer dynamics are not fully understood.