Rich dynamics and anticontrol of extinction in a prey–predator system

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)1421-1445
Journal / PublicationNonlinear Dynamics
Volume98
Issue number2
Online published14 Oct 2019
Publication statusPublished - Oct 2019

Abstract

This paper reveals some new and rich dynamics of a two-dimensional prey–predator system and to anticontrol the extinction of one of the species. For a particular value of the bifurcation parameter, one of the system variable dynamics is going to extinct, while another remains chaotic. To prevent the extinction, a simple anticontrol algorithm is applied so that the system or bits can escape from the vanishing trap. As the bifurcation parameter increases, the system presents quasiperiodic, stable, chaotic and also hyperchaotic orbits. Some of the chaotic attractors are Kaplan–Yorke type, in the sense that the sum of its Lyapunov exponents is positive. Also, atypically for undriven discrete systems, it is numerically found that, for some small parameter ranges, the system seemingly presents strange nonchaotic attractors. It is shown both analytically and by numerical simulations that the original system and the anticontrolled system undergo several Neimark–Sacker bifurcations. Beside the classical numerical tools for analyzing chaotic systems, such as phase portraits, time series and power spectral density, the ‘0–1’ test is used to differentiate regular attractors from chaotic attractors.

Research Area(s)

  • Anticontrol, Neimark–Sacker bifurcation, Prey–predator system, Strange nonchaotic attractor, ‘0–1’ test

Citation Format(s)

Rich dynamics and anticontrol of extinction in a prey–predator system. / Danca, Marius-F.; Fečkan, Michal; Kuznetsov, Nikolay; Chen, Guanrong.

In: Nonlinear Dynamics, Vol. 98, No. 2, 10.2019, p. 1421-1445.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review