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Discrete Memristive Conservative Chaotic Map: Dynamics, Hardware Implementation, and Application in Secure

Quanli Deng, Chunhua Wang, Yichuang Sun

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    Summary
    This summary is machine-generated.

    This study introduces a novel discrete memristor-based conservative chaotic map (DMCM) for secure communication. The DMCM demonstrates superior randomness and bit error rate performance compared to traditional dissipative chaotic maps.

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    Area of Science:

    • Chaos Theory
    • Nonlinear Dynamics
    • Secure Communications

    Background:

    • Randomness in chaotic systems is vital for secure communication.
    • Conservative chaotic systems offer better ergodicity and randomness than dissipative ones.
    • Memristor-based conservative chaotic maps have not been previously reported.

    Purpose of the Study:

    • To propose and analyze a novel volume-preserving chaotic map incorporating discrete memristors (DM).
    • To investigate the dynamical properties and hardware implementation of the proposed discrete memristive conservative map (DMCM).
    • To evaluate the performance of DMCM in secure communication applications.

    Main Methods:

    • Development of a generic conservative map model with DM integration.
    • Verification of conservative properties using the Jacobian matrix determinant.
    • Numerical analysis of dynamical behaviors (phase portraits, Lyapunov exponents, bifurcation diagrams) for four DM models.
    • Hardware implementation on an FPGA platform.

    Main Results:

    • The proposed map exhibits conservative characteristics.
    • Numerical simulations confirmed the memristive behavior of four distinct DM models.
    • The DMCM demonstrated reliable dynamical properties and successful hardware implementation.
    • Secure communication experiments showed improved bit error rate performance over classical dissipative maps.

    Conclusions:

    • The developed DMCM is a viable and effective tool for secure communication.
    • The integration of memristors into conservative chaotic maps opens new avenues for cryptographic applications.
    • DMCM offers enhanced security features due to its inherent randomness and ergodicity.