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Hyperchaos synchronization using univariate impulse control.

Kun Tian1, Chao Bai2, Hai-Peng Ren1,2

  • 1Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi'an University of Technology, Xi'an 710048, China.

Physical Review. E
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Summary
This summary is machine-generated.

This study introduces a univariate impulse control method for synchronizing two time-delayed hyperchaotic systems. The method ensures synchronization stability and asymptotic synchronization, validated by simulations and experiments.

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Area of Science:

  • Nonlinear Dynamics and Chaos Theory
  • Control Systems Engineering
  • Complex Systems Analysis

Background:

  • Rössler and Chen systems with time delay exhibit hyperchaotic behavior, characterized by multiple positive Lyapunov exponents and infinite dimensions.
  • Hyperchaos offers significant application potential, particularly in the field of hyperchaos synchronization.
  • Univariate impulse control presents an efficient method for system synchronization due to minimal perturbations, but synchronizing hyperchaotic systems remains challenging.

Purpose of the Study:

  • To propose a novel univariate impulse control method for synchronizing two time-delayed hyperchaotic systems.
  • To develop and prove a theorem establishing sufficient conditions for synchronization using this control method.
  • To demonstrate the method's effectiveness in guaranteeing asymptotic synchronization and its practical feasibility.

Main Methods:

  • Development of a univariate impulse control strategy tailored for time-delayed hyperchaotic systems.
  • Mathematical formulation and rigorous proof of a theorem outlining synchronization conditions.
  • Establishment of an upper bound for the impulse interval to ensure asymptotic synchronization.

Main Results:

  • A novel univariate impulse control method for synchronizing time-delayed hyperchaotic systems is successfully proposed.
  • A proven theorem provides sufficient conditions for achieving synchronization stability.
  • The derived upper bound on the impulse interval guarantees asymptotic synchronization.

Conclusions:

  • The proposed univariate impulse control method effectively synchronizes time-delayed hyperchaotic systems.
  • The theoretical analysis and experimental validation confirm the method's correctness and feasibility.
  • This work advances the understanding and application of control strategies for complex hyperchaotic dynamics.