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Coexisting Infinite Orbits in an Area-Preserving Lozi Map.

Houzhen Li1, Kexin Li1, Mo Chen1

  • 1School of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, China.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

This study reveals initial value-dependent coexisting infinite orbits in the discrete Lozi map, including periodic, quasi-periodic, and chaotic behaviors. Complexity analysis confirms these orbits are intricately linked to initial conditions.

Keywords:
coexisting orbitscomplexitydiscrete mapshardware platforminitial values

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Area of Science:

  • Dynamical systems and chaos theory.
  • Nonlinear dynamics and discrete systems.
  • Memristor-based circuit applications.

Background:

  • Extreme multistability with coexisting infinite orbits is common in continuous memristor systems.
  • Such phenomena are rarely observed in discrete dynamical systems.
  • Understanding discrete systems is crucial for developing novel chaotic circuits.

Purpose of the Study:

  • To investigate initial value-related coexisting infinite orbits in a discrete dynamical system.
  • To analyze the complexity and topological characteristics of these orbits.
  • To validate findings through a hardware implementation.

Main Methods:

  • Utilized bifurcation and phase orbit diagrams to identify coexisting infinite orbits.
  • Employed spectral entropy and sample entropy to quantify initial value-related complexity.
  • Developed a microprocessor-based hardware platform for experimental validation.

Main Results:

  • Discovered initial value-dependent coexisting infinite orbits in the area-preserving Lozi map.
  • Identified diverse orbit types including periodic, quasi-periodic, and chaotic behaviors.
  • Demonstrated complex complexity distributions intrinsically linked to initial values.

Conclusions:

  • The area-preserving Lozi map exhibits significant initial value-related multistability in discrete systems.
  • Coexisting infinite orbits display varied complexities dependent on initial conditions.
  • Hardware validation confirms the theoretical findings on initial value sensitivity.