A1 Journal article (refereed)
Rich dynamics and anticontrol of extinction in a prey–predator system (2019)

Danca, M.-F., Fečkan, M., Kuznetsov, N., & Chen, G. (2019). Rich dynamics and anticontrol of extinction in a prey–predator system. Nonlinear Dynamics, 98(2), 1421-1445. https://doi.org/10.1007/s11071-019-05272-3

JYU authors or editors

Publication details

All authors or editors: Danca, Marius-F.; Fečkan, Michal; Kuznetsov, Nikolay; Chen, Guanrong

Journal or series: Nonlinear Dynamics

ISSN: 0924-090X

eISSN: 1573-269X

Publication year: 2019

Volume: 98

Issue number: 2

Pages range: 1421-1445

Publisher: Springer

Publication country: Netherlands

Publication language: English

DOI: https://doi.org/10.1007/s11071-019-05272-3

Publication open access: Not open

Publication channel open access:

Publication is parallel published: https://arxiv.org/abs/1910.00235


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.

Keywords: chaos theory; bifurcation

Free keywords: prey–predator system; anticontrol Neimark–Sacker bifurcation; ‘0–1’ test; strange nonchaotic attractor

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2019

JUFO rating: 2

Last updated on 2021-09-06 at 06:11