Optimization of the Kaplan-Yorke dimension in fractional-order chaotic oscillators by metaheuristics
Abstract The optimization of the Kaplan-Yorke dimension ( D K Y ) of fractional-order chaotic oscillators (FOCOs) is shown herein by applying two metaheuristics, namely: differential evolution and particle swarm optimization algorithms. The optimization process is performed in two stages, and the cases of study are five commensurate (all derivatives have the same fractional-order) and incommensurate (all derivatives have different fractional-order) FOCOs. The first optimization stage evaluates the equilibrium points and eigenvalues of the individuals or particles to verify if they accomplish the minimum fractional-order value to guarantee chaotic behavior. The individuals or particles accomplishing this requirement are passed to the second optimization stage evaluating their D K Y . This saves computing time because the individuals or particles that do not accomplish the minimum fractional-order value, are not simulated in the time domain. We show that this optimization approach generates feasible values of the parameters of the FOCOs, providing better D K Y values compared to the ones already reported in the literature.