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Related Experiment Video

Updated: May 29, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Strongly perturbed bondorbital attractors for generalized systems.

A Dlamini1, E F Doungmo Goufo1, M Khumalo1

  • 1Department of Mathematical Sciences, University of South Africa, Florida 0003, South Africa.

Chaos (Woodbury, N.Y.)
|February 3, 2025
PubMed
Summary

This study explores chaotic systems with bondorbital attractors, examining both classical and fractional-order models. Fractional calculus, using the Caputo-Fabrizio operator, reveals complex dynamics and memory effects, validated by hardware implementation.

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Area of Science:

  • Nonlinear Dynamics and Chaos Theory
  • Fractional Calculus
  • Applied Mathematics

Background:

  • Chaotic systems exhibit complex dynamics, often visualized through attractors.
  • Generalized differential equations can model intricate systems.
  • Fractional calculus offers advanced tools for analyzing systems with memory effects.

Purpose of the Study:

  • To analyze a generalized chaotic system with bondorbital attractors.
  • To investigate both classical and fractional-order versions of the system.
  • To validate findings through analytical, numerical, and hardware implementations.

Main Methods:

  • Analytical and numerical examination of classical and fractional-order chaotic systems.
  • Convergence and stability analyses.
  • Field-programmable gate array (FPGA) based electric circuit implementation for hardware validation.

Main Results:

  • Confirmation of bondorbital attractors in the classical chaotic system.
  • Emergence of bondorbital attractors in the fractional-order system using the Caputo-Fabrizio operator.
  • Observed perturbations in fractional-order attractors and consistent hardware validation results.

Conclusions:

  • Fractional calculus, specifically the Caputo-Fabrizio operator, effectively captures memory effects in chaotic dynamics.
  • The study bridges theoretical modeling of chaotic systems with practical hardware applications.
  • Findings provide valuable insights for modeling complex systems in various scientific domains.