Estimating the Highest Time-Step in Numerical Methods to Enhance the Optimization of Chaotic Oscillators

Martín Alejandro Valencia-Ponce, Esteban Tlelo-Cuautle and Luis Gerardo de la Fraga
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Martín Alejandro Valencia-Ponce: Department of Electronics, INAOE, Tonantzintla, Puebla 72840, Mexico
Esteban Tlelo-Cuautle: Department of Electronics, INAOE, Tonantzintla, Puebla 72840, Mexico
Luis Gerardo de la Fraga: Computer Science Department, CINVESTAV, Av. IPN 2508, Mexico City 07360, Mexico

Mathematics, 2021, vol. 9, issue 16, 1-15

Abstract: The execution time that takes to perform numerical simulation of a chaotic oscillator mainly depends on the time-step h . This paper shows that the optimization of chaotic oscillators can be enhanced by estimating the highest h in either one-step or multi-step methods. Four chaotic oscillators are used as a case study, and the optimization of their Kaplan-Yorke dimension ( D K Y ) is performed by applying three metaheuristics, namely: particle swarm optimization (PSO), many optimizing liaison (MOL), and differential evolution (DE) algorithms. Three representative one-step and three multi-step methods are used to solve the four chaotic oscillators, for which the estimation of the highest h is obtained from their stability analysis. The optimization results show the effectiveness of using a high h value for the six numerical methods in reducing execution time while maximizing the positive Lyapunov exponent ( L E + ) and D K Y of the chaotic oscillators by applying PSO, MOL, and DE algorithms.

Keywords: chaotic oscillator; time-step; one-step method; multi-step method; particle swarm optimization (PSO); many optimizing liaison (MOL); differential evolution (DE); Kaplan-Yorke dimension; Lyapunov exponent (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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