Hopf Bifurcation, Hopf-Hopf Bifurcation, and Period-Doubling Bifurcation in a Four-Species Food Web
Joint Authors
Huang, Tousheng
Zhang, Huayong
Cong, Xuebing
Ma, Shengnan
Kang, Ju
Huang, Hai
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-21, 21 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-09-27
Country of Publication
Egypt
No. of Pages
21
Main Subjects
Abstract EN
Complex dynamics of a four-species food web with two preys, one middle predator, and one top predator are investigated.
Via the method of Jacobian matrix, the stability of coexisting equilibrium for all populations is determined.
Based on this equilibrium, three bifurcations, i.e., Hopf bifurcation, Hopf-Hopf bifurcation, and period-doubling bifurcation, are analyzed by center manifold theorem, bifurcation theorem, and numerical simulations.
We reveal that, influenced by the three bifurcations, the food web can exhibit very complex dynamical behaviors, including limit cycles, quasiperiodic behaviors, chaotic attractors, route to chaos, period-doubling cascade in orbits of period 2, 4, and 8 and period 3, 6, and 12, periodic windows, intermittent period, and chaos crisis.
However, the complex dynamics may disappear with the extinction of one of the four populations, which may also lead to collapse of the food web.
It suggests that the dynamical complexity and food web stability are determined by the food web structure and existing populations.
American Psychological Association (APA)
Zhang, Huayong& Kang, Ju& Huang, Tousheng& Cong, Xuebing& Ma, Shengnan& Huang, Hai. 2018. Hopf Bifurcation, Hopf-Hopf Bifurcation, and Period-Doubling Bifurcation in a Four-Species Food Web. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-21.
https://search.emarefa.net/detail/BIM-1209310
Modern Language Association (MLA)
Zhang, Huayong…[et al.]. Hopf Bifurcation, Hopf-Hopf Bifurcation, and Period-Doubling Bifurcation in a Four-Species Food Web. Mathematical Problems in Engineering No. 2018 (2018), pp.1-21.
https://search.emarefa.net/detail/BIM-1209310
American Medical Association (AMA)
Zhang, Huayong& Kang, Ju& Huang, Tousheng& Cong, Xuebing& Ma, Shengnan& Huang, Hai. Hopf Bifurcation, Hopf-Hopf Bifurcation, and Period-Doubling Bifurcation in a Four-Species Food Web. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-21.
https://search.emarefa.net/detail/BIM-1209310
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1209310