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Image of Discontinuity, Nonlinearity and Complexity
ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Delimitation of Hyperchaotic Regions in Parameter Planes of a Four-Dimensional Dynamical System

Discontinuity, Nonlinearity, and Complexity 8(4) (2019) 459--465 | DOI:10.5890/DNC.2019.12.009

Juliane C. Ramos, Paulo C. Rech

Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville, Brazil

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Abstract

We report results of a numerical investigation on parameter planes of a set of four autonomous first-order nonlinear ordinary differential equations. More specifically, here are reported ten numerically computed parameter plane diagrams for a five-parameter four-dimensional system, where the dynamical behavior of each point is characterized by using the related Lyapunov exponents spectrum. Each of these parameter plane diagrams indicates parameter values for which hyperchaos, chaos, quasiperiodicity, and periodicity may be found, i.e., each of these diagrams shows delimited regions for each of these dynamical behaviors.

Acknowledgments

The authors thank Conselho Nacional de Desenvolvimento Científico e Tecnológico-CNPq, and Fundação de Amparo à Pesquisa e Inovação do Estado de Santa Catarina-FAPESC, Brazilian Agencies, for financial support.

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