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Numerical analysis and circuit implementation of new nonlinear dynamic systems of the Lorentz-like type of fractional order
  • Michael Kopp
Michael Kopp

Corresponding Author:[email protected]

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Abstract

In this study, novel Lorentz-like fractional-order dynamical systems are proposed, offering potential applications across various engineering domains. Based on a threedimensional system of the Lorentz-like type of integer order, new nonlinear dynamic systems of fractional order are constructed for four, five, and six state variables. These systems can describe real convective processes in fractal media characterized by a memory effect. For these systems, equilibrium points and stability conditions are determined using the theorem on local asymptotic stability of fractional order systems. Utilizing the frequency domain approximation method, Matlab-Simulink models were developed for novel chaos generators characterized by a fractional order index of 0.95. Through the utilization of Multisim software, we designed electronic circuits to validate the physical feasibility of our proposed systems. The simulation results obtained from both Matlab and Multisim exhibit excellent agreement, reinforcing the reliability of our proposed models. To demonstrate the synchronization of two unidirectionally coupled 3.8d chaotic systems, Matlab-Simulink models were created in two versions. The first version assumes an identical fractional index for both the master and slave systems, while the second version involves different fractional indices for the two systems. These systems were further employed for the chaotic masking of a harmonic signal. An electronic circuit implementing the chaotic masking process in Multisim is also presented. The results obtained from this proposed scheme demonstrate the success of the approach in accomplishing the encryption and decryption procedures effectively.
20 Feb 2024Submitted to TechRxiv
20 Feb 2024Published in TechRxiv