Eur. Phys. J. B (2017) 90: 251
https://doi.org/10.1140/epjb/e2017-80533-5

Regular Article

Hyperchaos and quasiperiodicity from a four-dimensional system based on the Lorenz system

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

^a e-mail: paulo.rech@udesc.br

Received: 19 September 2017
Received in final form: 17 October 2017
Published online: 13 December 2017

Abstract

This paper reports on numerically computed parameter plane plots for a dynamical system modeled by a set of five-parameter, four autonomous first-order nonlinear ordinary differential equations. The dynamical behavior of each point, in each parameter plane, is characterized by Lyapunov exponents spectra. Each of these diagrams indicates parameter values for which hyperchaos, chaos, quasiperiodicity, and periodicity may be found. In fact, each diagram shows delimited regions where each of these behaviors happens. Moreover, it is shown that some of these parameter planes display organized periodic structures embedded in quasiperiodic and chaotic regions.