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

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.

Analysis of New 4D Hyperchaotic Systems MACM and Implementation Using Runge-kutta

“…The NHS system is built by inspecting, modifying and adding one state to the MACM chaotic system [14]. The proposed NHS is described as follows (1) In this work, we firstly introduce a new 4D hyperchaotic system (NHS) via modifying 3D MACM system inspired by the above works [15]. Two critical parameters, only two nonlinearities, flexible and robust, one unstable equilibrium saddle-point, and low-cost electronic implementation for the continuous and discretized versions are the main novelties of the proposed hyperchaotic system.…”

Enhancing the emergence of hyperchaos using an indirect coupling and its verification based on digital implementation

“…This section validates the enhancement of hyperchaos emergence using an indirect coupling. The digital implementation of the systems ( 9)-( 10) using an indirect coupling (5)-( 8) is designed using C code compiler of MikroC PRO for dsPIC30/33 and PIC24 [11][12][13][14][15]. Two PIC-24FJ64GA006 microcontrollers are used to implement each system with their respective indirect coupling separately in order to achieve the emergence of hyperchaos.…”

Chaotic Motion Planning for Mobile Robots: Progress, Challenges, and Opportunities

“…There are also additional challenges towards real-world implementations such as simulating the continuous chaotic systems discussed in Section III. As the systems are chaotic, the system states evolution through time needs to be solved numerically which leads to chaotic degradation [214]. Chaotic degradation is the rise in error of the simulated trajectory in chaotic dynamical system from a true trajectory given any initial state.…”