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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • Multistability in chaotic systems is typically classified by attractor count, shape, and origin.
  • Combinations of multiple multistability types are seldom investigated.
  • Understanding complex multistability is crucial for advancing chaos theory.

Purpose of the Study:

  • To propose a technique for constructing Lurie systems with simultaneous megastability, matryoshka multistability, and symmetric twin attractors.
  • To explore systems with infinite 1D or 2D lattices of infinitely nested, self-similar twin attractors.
  • To provide a framework for developing systems with combined multistability.

Main Methods:

  • Construction of Lurie systems by manipulating nonlinear functions.
  • Utilizing periodic behavior for 1D lattices, log-periodic behavior for nested attractors, and symmetry for twin attractors.
  • Employing offset boosting for 2D attractor lattices.

Main Results:

  • Demonstration of systems exhibiting three simultaneous types of multistability: megastability, matryoshka multistability, and symmetric twin attractors.
  • Observation of infinite 1D or 2D lattices of infinitely nested, self-similar twin attractors.
  • All attractors were found to be hidden, requiring specific initial conditions.

Conclusions:

  • The proposed technique successfully generates chaotic systems with combined multistability.
  • The findings offer deep insights into the nature of megastability, matryoshka multistability, and symmetric twin attractors.
  • This work provides a foundation for further research into complex multistability in chaotic systems.