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This study introduces a discrete memristor model coupled with a sine chaotic map. The research explores complex dynamics and validates a novel image encryption algorithm, demonstrating memristor applications in chaotic systems.

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Memristor Applications

Background:

  • Continuous-time memristors are utilized in chaotic circuits.
  • Discrete memristor models offer potential for discrete chaotic maps.
  • Further investigation into discrete memristor-coupled chaotic systems is warranted.

Purpose of the Study:

  • To propose and analyze a discrete memristor model.
  • To couple this model with a 1D sine chaotic map to generate 2D chaotic maps.
  • To investigate the complex dynamics and potential applications, such as image encryption.

Main Methods:

  • Development of a discrete memristor model and analysis of its voltage-current characteristics.
  • Coupling the discrete memristor with a 1D sine chaotic map using various frameworks.
  • Employing analytical methods and numerical experiments to study dynamic behaviors and parameter control.
  • Designing and evaluating an image encryption algorithm based on the memristor-coupled chaotic map.

Main Results:

  • Two distinct 2D memristor-coupled chaotic map models were generated.
  • Different coupling frameworks lead to varied complex dynamical behaviors.
  • Parameter variations enrich dynamics and increase the complexity of the memristor-coupled sine map.
  • The developed encryption algorithm demonstrates strong image encryption capabilities.

Conclusions:

  • The proposed discrete memristor model and its coupling with chaotic maps generate complex dynamics.
  • Parameter control significantly influences the richness and complexity of chaotic behaviors.
  • The memristor-based chaotic map offers a promising foundation for secure image encryption applications.
  • Hardware experiments verified the numerical findings, confirming the model's practical viability.