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Intermingled basins in coupled Lorenz systems.

Sabrina Camargo1, Ricardo L Viana, Celia Anteneodo

  • 1Department of Physics, PUC-Rio, Rio de Janeiro, Brazil.

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Two coupled Lorenz oscillators synchronize chaotically. Their complex dynamics reveal intermingled basins of attraction, where synchronization and antisynchronization states are intricately mixed, with quantitative scaling laws describing this phenomenon.

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Area of Science:

  • Nonlinear dynamics
  • Chaos theory
  • Complex systems

Background:

  • Lorenz oscillators are fundamental models for chaotic behavior.
  • Coupled chaotic systems can exhibit complex synchronization patterns.
  • Intermingled basins of attraction present intricate dynamics in nonlinear systems.

Purpose of the Study:

  • To investigate synchronization and antisynchronization in coupled Lorenz oscillators.
  • To analyze the phenomenon of intermingled basins of attraction.
  • To quantitatively characterize the riddling of basins using scaling laws.

Main Methods:

  • Analysis of a system of two identical linearly coupled Lorenz oscillators.
  • Verification of mathematical conditions for intermingled basins of attraction.
  • Derivation of scaling laws to describe basin riddling.

Main Results:

  • Identified a range of coupling strength for chaotic synchronization.
  • Confirmed the existence of global synchronization and antisynchronization attractors.
  • Demonstrated intermingled basins where attractors are riddled with each other's basins.
  • Obtained scaling laws characterizing the degree of basin riddling.

Conclusions:

  • Coupled Lorenz oscillators exhibit complex synchronization phenomena, including intermingled basins.
  • The study provides a quantitative framework for understanding basin riddling in chaotic systems.
  • Findings contribute to the broader understanding of complex dynamics in coupled nonlinear systems.