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Initial-switched boosting bifurcations in 2D hyperchaotic map.

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This study introduces a new discrete-time hyperchaotic map. It demonstrates how initial conditions can control complex dynamics, enabling applications in chaos-based engineering.

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • Initial-boosting attractors in continuous-time systems are gaining attention.
  • Implementing such attractors in discrete-time maps presents a challenge.

Purpose of the Study:

  • To propose a novel two-dimensional (2D) hyperchaotic map for discrete-time systems.
  • To investigate the parameter-dependent and initial-boosting bifurcations in this map.
  • To explore the control of complex dynamics via initial conditions.

Main Methods:

  • Development of a simple algebraic 2D hyperchaotic map.
  • Analysis of two special cases: line and no fixed points.
  • Employing numerical methods to study bifurcations.
  • Hardware implementation on a microcontroller platform.

Main Results:

  • The proposed 2D hyperchaotic map exhibits complex dynamics like hyperchaos, chaos, and periodic behaviors.
  • Parameter and initial conditions significantly influence these dynamics.
  • Crucially, initial conditions can switch boosting bifurcations, controlling dynamic amplitudes.
  • Hardware validation confirmed the generation of initial-switched boosting hyperchaos/chaos.

Conclusions:

  • A novel 2D hyperchaotic map is presented, capable of initial-boosting attractors in discrete-time systems.
  • The map's dynamics are controllable via initial conditions, offering potential for chaos-based engineering.
  • Hardware implementation validates the theoretical findings.