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In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
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A Robust Memristor-Enhanced Polynomial Hyper-Chaotic Map and Its Multi-Channel Image Encryption Application.

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This study introduces a novel memristor-enhanced hyper-chaotic map for secure image encryption. The proposed system demonstrates superior chaotic dynamics and robust security features for efficient data protection.

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Area of Science:

  • Nonlinear Dynamics and Chaos Theory
  • Solid-State Circuits and Devices
  • Information Security and Cryptography

Background:

  • Memristors are increasingly utilized to improve the dynamic properties of chaotic systems.
  • Designing novel chaotic maps with enhanced complexity is crucial for secure communication.

Purpose of the Study:

  • To design and analyze a novel 2D memristor-enhanced polynomial hyper-chaotic map (2D-MPHM).
  • To evaluate the dynamical properties and complexity of the 2D-MPHM.
  • To apply the 2D-MPHM to a multi-channel image encryption algorithm (MIEA-MPHM) and assess its security and efficiency.

Main Methods:

  • Design of a 2D-MPHM using cross-coupled TiO2 memristors.
  • Analysis of dynamical properties via Lyapunov exponents, bifurcation diagrams, and trajectory diagrams.
  • Complexity evaluation using Kolmogorov and sample entropy.
  • Application to a multi-channel image encryption algorithm (MIEA-MPHM) with comprehensive security and efficiency testing.

Main Results:

  • The 2D-MPHM exhibits superior dynamical properties and complexity compared to existing maps.
  • The MIEA-MPHM demonstrates excellent security, including large key space, high sensitivity, and strong resistance to attacks.
  • The MIEA-MPHM achieves a high average encryption rate of up to 87.2798 Mbps, indicating significant efficiency.

Conclusions:

  • The proposed 2D-MPHM offers enhanced chaotic behavior suitable for cryptographic applications.
  • The MIEA-MPHM provides a secure and efficient solution for multi-channel image encryption.
  • This research contributes to the advancement of memristor-based chaotic systems for information security.