Hyperchaotic states in the parameter-space |
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Authors: | Marcos J CorreiaPaulo C Rech |
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Institution: | Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville, Brazil |
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Abstract: | In this paper we propose a numerical method to characterize hyperchaotic points in the parameter-space of continuous-time dynamical systems. The method considers the second largest Lyapunov exponent value as a measure of hyperchaotic motion, to construct two-dimensional parameter-space color plots. Different levels of hyperchaos in these plots are represented by a continuously changing yellow-red scale. As an example, a particular system modeled by a set of four nonlinear autonomous first-order ordinary differential equations is considered. Practical applications of these plots include, by instance, walking in the parameter-space of hyperchaotic systems along desirable paths. |
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Keywords: | Parameter-space Lyapunov exponents Chaos Hyperchaos Nonlinear differential equations |
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