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  • Open Access

    ARTICLE

    Numerical Simulation of the Fractional-Order Lorenz Chaotic Systems with Caputo Fractional Derivative

    Dandan Dai1, Xiaoyu Li2, Zhiyuan Li2, Wei Zhang3, Yulan Wang2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 1371-1392, 2023, DOI:10.32604/cmes.2022.022323 - 27 October 2022

    Abstract Although some numerical methods of the fractional-order chaotic systems have been announced, high-precision numerical methods have always been the direction that researchers strive to pursue. Based on this problem, this paper introduces a high-precision numerical approach. Some complex dynamic behavior of fractional-order Lorenz chaotic systems are shown by using the present method. We observe some novel dynamic behavior in numerical experiments which are unlike any that have been previously discovered in numerical experiments or theoretical studies. We investigate the influence of , , on the numerical solution of fractional-order Lorenz chaotic systems. The simulation results More >

  • Open Access

    ARTICLE

    Secure Communication Scheme based on A New Hyperchaotic System

    Khaled Benkouider1, Aceng Sambas2, Ibrahim Mohammed Sulaiman3, Mustafa Mamat4, Kottakkaran Sooppy Nisar5,*

    CMC-Computers, Materials & Continua, Vol.73, No.1, pp. 1019-1035, 2022, DOI:10.32604/cmc.2022.025836 - 18 May 2022

    Abstract This study introduces a new continuous time differential system, which contains ten terms with three quadratic nonlinearities. The new system can demonstrate hyperchaotic, chaotic, quasi-periodic, and periodic behaviors for its different parameter values. All theoretical and numerical analysis are investigated to confirm the complex hyperchaotic behavior of our proposed model using many tools that include Kaplan-Yorke dimension, equilibrium points stability, bifurcation diagrams, and Lyapunov exponents. By means of Multisim software, the authors also designed an electronic circuit to confirm our proposed systems’ physical feasibility. MATLAB and Multisim simulation results excellently agree with each other, which More >

  • Open Access

    ARTICLE

    Fixed-Time Adaptive Time-Varying Matrix Projective Synchronization of Time-Delayed Chaotic Systems with Different Dimensions

    Peng Zheng1, Xiaozhen Guo2,*, Guoguang Wen3

    CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.3, pp. 1451-1463, 2022, DOI:10.32604/cmes.2022.019769 - 19 April 2022

    Abstract This paper deals with the fixed-time adaptive time-varying matrix projective synchronization (ATVMPS) of different dimensional chaotic systems (DDCSs) with time delays and unknown parameters. Firstly, to estimate the unknown parameters, adaptive parameter updated laws are designed. Secondly, to realize the fixed-time ATVMPS of the time-delayed DDCSs, an adaptive delay-unrelated controller is designed, where time delays of chaotic systems are known or unknown. Thirdly, some simple fixed-time ATVMPS criteria are deduced, and the rigorous proof is provided by employing the inequality technique and Lyapunov theory. Furthermore, the settling time of fixed-time synchronization (Fix-TS) is obtained, which More >

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