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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • Multistability is a phenomenon where multiple stable states coexist in a dynamical system.
  • Discrete chaotic systems often exhibit complex behaviors, but multistability with diverse attractors is less common.
  • Hyperchaotic systems possess more than one positive Lyapunov exponent, indicating higher complexity.

Purpose of the Study:

  • To investigate the dynamical behavior of an M-dimensional nonlinear hyperchaotic model (M-NHM).
  • To analyze the occurrence and types of multistability within the M-NHM.
  • To develop a method to overcome chaos degradation in multistability regions.

Main Methods:

  • Numerical simulations were used to explore the M-NHM.
  • Analysis of phase portraits and Lyapunov exponents to identify different types of attractors.
  • Introduction of a simple controller to modify the system's dynamics.

Main Results:

  • The M-NHM exhibits multistability with four types of coexisting attractors: single limit cycle, cluster of limit cycles, single hyperchaotic attractor, and cluster of hyperchaotic attractors.
  • Both asymmetric and symmetric properties were observed for coexisting attractors within the same parameter set.
  • A controller was successfully implemented to enhance chaotic behavior, counteracting degradation in multistability regions.

Conclusions:

  • The M-NHM demonstrates rich dynamical behaviors, including unusual forms of multistability in discrete chaotic systems.
  • The proposed controller effectively improves chaotification in the presence of multistability.
  • This research contributes to understanding complex dynamics in nonlinear and hyperchaotic systems.