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Synchronization in chaotic systems is affected by dissipation levels. Low dissipation leads to complex synchronization dynamics, while high dissipation simplifies it, impacting parameter mismatch effects.

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Area of Science:

  • Complex Systems and Nonlinear Dynamics
  • Chaos Theory and Synchronization

Background:

  • Synchronization is a widespread phenomenon in dynamical systems, yet its study in low-dissipation regimes remains underexplored.
  • Understanding how dissipation influences synchronization is crucial for characterizing complex system behavior.

Purpose of the Study:

  • To investigate the impact of varying dissipation levels on the synchronization of coupled chaotic oscillators.
  • To analyze how parameter or frequency mismatches affect synchronizability across different dissipation regimes.

Main Methods:

  • Utilized paradigmatic chaotic systems: Rössler (strong dissipation), Lorenz 84 (weak dissipation), and Sprott A (non-dissipative).
  • Computed Shannon entropy from recurrence plots to quantify the complexity of synchronized dynamics.
  • Analyzed the structure of the joint attractor under parameter or frequency mismatch.

Main Results:

  • Strongly dissipative systems show synchronization dynamics compatible with average parameter mismatch.
  • Weakly dissipative systems exhibit more complex synchronization with higher Shannon entropy values.
  • Non-dissipative (conservative) systems display simpler dynamics, either similar chaotic behavior or periodic ones.

Conclusions:

  • Dissipation level significantly alters the nature of synchronization and its response to parameter mismatch in chaotic systems.
  • Shannon entropy effectively characterizes the complexity of synchronized dynamics across different dissipation regimes.
  • The findings highlight distinct synchronization behaviors in strongly dissipative, weakly dissipative, and conservative chaotic systems.