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Static and dynamic attractive-repulsive interactions in two coupled nonlinear oscillators.

Shiva Dixit1, Manish Dev Shrimali1

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Dynamic and static attractive-repulsive interactions can shift nonlinear oscillators from oscillatory to steady states. This study analyzes these transitions in coupled oscillators, offering insights into system dynamics.

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Complex Systems

Background:

  • Systems often display both attractive and repulsive interactions, which can be dynamic or static.
  • Understanding systems with dynamically switching interactions is crucial for practical applications.
  • Such systems can be modeled using coexisting competing interactions.

Purpose of the Study:

  • Investigate the impact of time-varying attractive-repulsive interactions.
  • Analyze a hybrid model of coexisting attractive-repulsive interactions in coupled nonlinear oscillators.
  • Examine dynamical transitions in limit cycle and chaotic oscillators.

Main Methods:

  • Studied dynamics of two coupled nonlinear oscillators.
  • Analyzed time-varying attractive-repulsive interactions.
  • Investigated a hybrid model of coexisting attractive-repulsive interactions.
  • Employed linear stability analysis for analytical conditions.

Main Results:

  • Dynamic or static attractive-repulsive interactions induce transitions from oscillatory to steady states in identical nonlinear oscillators.
  • Analytical conditions for stable steady states in dynamic (low switching period) and static interactions were derived and validated numerically.
  • Oscillations can be revived at higher interaction strengths with a high switching period.

Conclusions:

  • Attractive-repulsive interactions significantly influence the dynamics of coupled nonlinear oscillators.
  • The study provides analytical conditions for steady states, validated by numerical simulations.
  • Switching time period and interaction strength are key parameters determining system behavior.