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Additional complex conjugate feedback-induced explosive death and multistabilities.

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Area of Science:

  • Nonlinear dynamics and complex systems
  • Coupled oscillator networks
  • Feedback control systems

Background:

  • Feedback is crucial for natural and man-made systems.
  • Stuart-Landau oscillators are a fundamental model for studying oscillations.
  • Understanding emergent dynamics in coupled systems is an ongoing challenge.

Purpose of the Study:

  • To investigate the effects of additional complex conjugate feedback on globally coupled Stuart-Landau oscillators.
  • To identify novel dynamical behaviors induced by this feedback.
  • To characterize the transitions and stability of these emergent states.

Main Methods:

  • Global coupling of Stuart-Landau oscillators with complex conjugate feedback.
  • Analysis of symmetry breaking and out-of-phase clusters.
  • Characterization of explosive amplitude death and multistability using amplitude order parameters.
  • Investigation of hysteresis in transitions.
  • Mapping global dynamical transitions in parametric spaces.
  • Bifurcation analysis and basin stability exploration of a reduced model.

Main Results:

  • Onset of symmetry breaking clusters and out-of-phase clusters.
  • Observation of explosive amplitude death and disparate multistable states.
  • First-order phase transition to explosive death, exhibiting hysteresis.
  • Detailed mapping of global dynamical transitions across parametric spaces.
  • Identification of bifurcation scenarios and basin stability characteristics.

Conclusions:

  • Additional complex conjugate feedback significantly alters the dynamics of coupled Stuart-Landau oscillators.
  • The study reveals new phenomena like explosive amplitude death and complex cluster formations.
  • The findings provide insights into emergent dynamics and control in complex systems.