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A physically extended Lorenz system.

Sungju Moon1, Jaemyeong Mango Seo1, Beom-Soon Han1

  • 1School of Earth and Environmental Sciences, Seoul National University, Seoul 08826, South Korea.

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Summary
This summary is machine-generated.

Researchers extended the Lorenz system to a six-dimensional model, incorporating rotation and scalar effects in fluid dynamics. This enhanced model reveals altered chaotic dynamics and self-synchronization capabilities, expanding our understanding of complex systems.

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Area of Science:

  • Fluid Dynamics
  • Nonlinear Systems
  • Chaos Theory

Background:

  • The Lorenz system models atmospheric convection.
  • Rayleigh-Bénard convection is a fundamental fluid dynamics phenomenon.
  • Limited parameters in the original Lorenz system restrict its applicability.

Purpose of the Study:

  • To extend the Lorenz system by incorporating rotation and a density-affecting scalar.
  • To investigate the impact of these additions on system dynamics and chaotic behavior.
  • To compare the extended system's behavior with the original Lorenz system.

Main Methods:

  • Derivation of a six-dimensional nonlinear ordinary differential equation system.
  • Numerical analysis of system behavior under varying parameters.
  • Comparison of bifurcation points and solution types (chaotic, periodic, intermittent) between the original and extended systems.

Main Results:

  • Significant shifts in bifurcation points within the thermal Rayleigh parameter space were observed.
  • The range of parameters yielding chaotic, periodic, and intermittent solutions was extended.
  • Rotation parameter increases neutralized chaos; scalar parameter increases generated new chaotic attractors.
  • The six-dimensional system demonstrated self-synchronization, requiring only solution transfer to one variable.

Conclusions:

  • The extended Lorenz system offers a richer dynamic behavior than the original.
  • Rotation and scalar effects introduce distinct modifications to fluid convection models.
  • The self-synchronization property of the extended system presents novel avenues for research in complex systems.