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Degradation Analysis of Chaotic Systems and their Digital Implementation in Embedded Systems

Author

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  • Rodrigo Méndez-Ramírez
  • Adrian Arellano-Delgado
  • Miguel Murillo-Escobar
  • César Cruz-Hernández

Abstract

Digital implementation of chaotic systems (CSs) has attracted increasing attention from researchers due to several applications in engineering, e.g., in areas as cryptography and autonomous mobile robots, where the properties of chaotic systems are strongly related. The CSs in the continuous version (CV) need to be discretized where chaotic degradation must be analyzed to guarantee preservation of chaos. In this paper, we present a degradation analysis of five three-dimensional CSs and the necessary conditions to implement the discretized versions (DVs) of Lorenz, Rössler, Chen, Liu and Chen, and Méndez-Arellano-Cruz-Martínez (MACM) CSs. Analytical and numerical analyses of chaos degradation are conducted by using the time series method; the maximum discrete step size and the Lyapunov Exponents (LEs) are computed by using the Euler, Heun, and fourth-order Runge–Kutta (RK4) numerical algorithms (NAs). We conducted comparative studies of performance based on time complexity of the five proposed CSs in their DVs by using four embedded systems (ESs) based on three families of Microchip microcontrollers 8-bit PIC16F, 16-bit dsPIC33FJ, and 32-bit PIC32MZ (of low-cost electronic implementation) and a Field Programmable Gate Array (FPGA). Based on the results, the intervals at control parameters to guarantee chaos are proposed, which improves the performance characteristics of the five proposed CSs in their DVs based on digital applications.

Suggested Citation

  • Rodrigo Méndez-Ramírez & Adrian Arellano-Delgado & Miguel Murillo-Escobar & César Cruz-Hernández, 2019. "Degradation Analysis of Chaotic Systems and their Digital Implementation in Embedded Systems," Complexity, Hindawi, vol. 2019, pages 1-22, December.
    • Handle: RePEc:hin:complx:9863982
    DOI: 10.1155/2019/9863982
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    References listed on IDEAS

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    1. Li Xiong & Yanjun Lu & Yongfang Zhang & Xinguo Zhang, 2019. "A Novel Memductor-Based Chaotic System and Its Applications in Circuit Design and Experimental Validation," Complexity, Hindawi, vol. 2019, pages 1-17, January.
    2. Chuanfu Wang & Chunlei Fan & Kai Feng & Xin Huang & Qun Ding, 2018. "Analysis of the Time Series Generated by a New High-Dimensional Discrete Chaotic System," Complexity, Hindawi, vol. 2018, pages 1-11, August.
    3. Apostolos Argyris & Dimitris Syvridis & Laurent Larger & Valerio Annovazzi-Lodi & Pere Colet & Ingo Fischer & Jordi García-Ojalvo & Claudio R. Mirasso & Luis Pesquera & K. Alan Shore, 2005. "Chaos-based communications at high bit rates using commercial fibre-optic links," Nature, Nature, vol. 438(7066), pages 343-346, November.
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