Rich dynamics and anticontrol of extinction in a prey–predator system
Year of publication
2019
Authors
Danca, Marius-F.; Fečkan, Michal; Kuznetsov, Nikolay; Chen, Guanrong
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.
Show moreOrganizations and authors
University of Jyväskylä
Kuznetsov Nikolay
Publication type
Publication format
Article
Parent publication type
Journal
Article type
Original article
Audience
ScientificPeer-reviewed
Peer-ReviewedMINEDU's publication type classification code
A1 Journal article (refereed), original researchPublication channel information
Journal
Publisher
Volume
98
Issue
2
Pages
1421-1445
ISSN
Publication forum
Publication forum level
2
Open access
Open access in the publisher’s service
No
Self-archived
Yes
Other information
Fields of science
Mathematics
Keywords
[object Object],[object Object]
Publication country
Netherlands
Internationality of the publisher
International
Language
English
International co-publication
Yes
Co-publication with a company
No
DOI
10.1007/s11071-019-05272-3
The publication is included in the Ministry of Education and Culture’s Publication data collection
Yes