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Optimizing the Kaplan–Yorke Dimension of Chaotic Oscillators Applying DE and PSO

1
Department of Electronics, National Institute for Astrophysics, Optics, and Electronics (INAOE), Tonantzintla, Puebla 72840, Mexico
2
Department of Computer Science, National Institute for Astrophysics, Optics, and Electronics (INAOE), Tonantzintla, Puebla 72840, Mexico
3
Department of Computer Science, Center for Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV), San Pedro Zacatenco, Ciudad de México 07360, Mexico
*
Author to whom correspondence should be addressed.
Technologies 2019, 7(2), 38; https://doi.org/10.3390/technologies7020038
Received: 20 March 2019 / Revised: 15 April 2019 / Accepted: 25 April 2019 / Published: 27 April 2019
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Abstract

When a new chaotic oscillator is introduced, it must accomplish characteristics like guaranteeing the existence of a positive Lyapunov exponent and a high Kaplan–Yorke dimension. In some cases, the coefficients of a mathematical model can be varied to increase the values of those characteristics but it is not a trivial task because a very huge number of combinations arise and the required computing time can be unreachable. In this manner, we introduced the optimization of the Kaplan–Yorke dimension of chaotic oscillators by applying metaheuristics, e.g., differential evolution (DE) and particle swarm optimization (PSO) algorithms. We showed the equilibrium points and eigenvalues of three chaotic oscillators that are simulated applying ODE45, and the Kaplan–Yorke dimension was evaluated by Wolf’s method. The chaotic time series of the state variables associated to the highest Kaplan–Yorke dimension provided by DE and PSO are used to encrypt a color image to demonstrate that they are useful in implementing a secure chaotic communication system. Finally, the very low correlation between the chaotic channel and the original color image confirmed the usefulness of optimizing Kaplan–Yorke dimension for cryptographic applications. View Full-Text
Keywords: chaos; PSO; DE; Kaplan–Yorke dimension chaos; PSO; DE; Kaplan–Yorke dimension
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Silva-Juarez, A.; Rodriguez-Gomez, G.; de la Fraga, L.G.; Guillen-Fernandez, O.; Tlelo-Cuautle, E. Optimizing the Kaplan–Yorke Dimension of Chaotic Oscillators Applying DE and PSO. Technologies 2019, 7, 38.

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