Optimization of Integer/Fractional Order Chaotic Systems by Metaheuristics and their Electronic Realization

Mathematicians have developed chaotic systems modeled by integer or fractional-order differential equations that can generate chaos or hyperchaos. Numerical methods to simulate these systems are different and require estimating step-size and memory length. Optimization loops are used to maximize positive Lyapunov exponents,Kaplan-Yorke dimension,and entropy,and the optimized models can be implemented using various technologies. The book covers applications of chaotic oscillators in random bit/number generators,cryptography,secure communications,robotics,and Internet of Things.

\n Format: Hardback
\n Length: 256 pages
\n Publication date: 10 May 2021
\n Publisher: Taylor & Francis Ltd
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Mathematicians have developed intricate chaotic systems, modeled by integer or fractional-order differential equations, that possess the ability to generate chaos or hyperchaos. These mathematical models can be simulated using numerical techniques, which differ significantly from those used for ordinary differential equations. The accuracy of these methods is crucial in assessing characteristics such as Lyapunov exponents, Kaplan-Yorke dimension, and entropy. One challenge in simulating these systems is determining the appropriate step size for the numerical method. This can be achieved by analyzing the eigenvalues of self-excited attractors, while evaluating the equilibrium points necessary for formulating Jacobian matrices is more complex for hidden attractors. Time simulation of fractional-order chaotic oscillators necessitates estimating a memory length to obtain precise results, which is closely related to memories in hardware design. Consequently, simulating chaotic/hyperchaotic oscillators of integer/fractional-order, with self-excited/hidden attractors, is essential for evaluating their Lyapunov exponents, Kaplan-Yorke dimension, and entropy. Furthermore, optimizing the main characteristics of these oscillators through metaheuristics, which involves varying the values of coefficients in a mathematical model, can enhance their dynamics. The optimized models can then be implemented using a wide range of technologies, including commercially available amplifiers, field-programmable analog arrays (FPAAs), field-programmable gate arrays (FPGA), microcontrollers, graphic processing units, and even nanometer technology of integrated circuits.

\n Weight: 548g\n
Dimension: 159 x 241 x 22 (mm)\n
ISBN-13: 9780367486686\n \n