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This study introduces a novel multiscroll chaotic system featuring two stable equilibrium points, a new category of hidden attractors. This breakthrough expands the understanding of complex dynamical systems and their potential applications.

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • Multiscroll hidden attractors are a recent research focus.
  • Existing studies primarily feature hidden attractors without equilibrium points.
  • Multiscroll hidden attractors with stable equilibrium points remain unreported.

Purpose of the Study:

  • To propose a novel multiscroll chaotic system with two stable equilibrium points.
  • To demonstrate the generation of multiscroll hidden attractors with stable equilibrium points.
  • To analyze the dynamical characteristics and experimental validation of the proposed system.

Main Methods:

  • Development of a new chaotic system incorporating a nonlinear function with breakpoints.
  • Analysis of dynamical behaviors using Lyapunov exponents, bifurcation diagrams, and Poincaré maps.
  • Implementation of the system using electronic circuits for hardware verification.

Main Results:

  • The proposed system generates multiscroll hidden attractors with two stable node-foci equilibrium points.
  • The number of scrolls can be controlled by adjusting breakpoints in the nonlinear function.
  • Numerical simulations and hardware experiments show consistent results, validating the system's behavior.

Conclusions:

  • This work presents the first reported multiscroll hidden attractors with stable equilibrium points.
  • The novel system offers a new platform for studying complex dynamics and hidden attractors.
  • The findings have implications for the design and application of chaotic systems.