The Gestation Delay: A Factor Causing Complex Dynamics in Gause-Type Competition Models
Joint Authors
Upadhyay, Ranjit Kumar
Agrawal, Rashmi
Datta, Jyotiska
Zhang, Zizhen
Source
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-21, 21 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-11-07
Country of Publication
Egypt
No. of Pages
21
Main Subjects
Abstract EN
In this paper, we consider a Gause-type model system consisting of two prey and one predator.
Gestation period is considered as the time delay for the conversion of both the prey and predator.
Bobcats and their primary prey rabbits and squirrels, found in North America and southern Canada, are taken as an example of an ecological system.
It has been observed that there are stability switches and the system becomes unstable due to the effect of time delay.
Positive invariance, boundedness, and local stability analysis are studied for the model system.
Conditions under which both delayed and nondelayed model systems remain globally stable are found.
Criteria which guarantee the persistence of the delayed model system are derived.
Conditions for the existence of Hopf bifurcation at the nonzero equilibrium point of the delayed model system are also obtained.
Formulae for the direction, stability, and period of the bifurcating solution are conducted using the normal form theory and center manifold theorem.
Numerical simulations have been shown to analyze the effect of each of the parameters considered in the formation of the model system on the dynamic behavior of the system.
The findings are interesting from the application point of view.
American Psychological Association (APA)
Zhang, Zizhen& Upadhyay, Ranjit Kumar& Agrawal, Rashmi& Datta, Jyotiska. 2018. The Gestation Delay: A Factor Causing Complex Dynamics in Gause-Type Competition Models. Complexity،Vol. 2018, no. 2018, pp.1-21.
https://search.emarefa.net/detail/BIM-1132928
Modern Language Association (MLA)
Zhang, Zizhen…[et al.]. The Gestation Delay: A Factor Causing Complex Dynamics in Gause-Type Competition Models. Complexity No. 2018 (2018), pp.1-21.
https://search.emarefa.net/detail/BIM-1132928
American Medical Association (AMA)
Zhang, Zizhen& Upadhyay, Ranjit Kumar& Agrawal, Rashmi& Datta, Jyotiska. The Gestation Delay: A Factor Causing Complex Dynamics in Gause-Type Competition Models. Complexity. 2018. Vol. 2018, no. 2018, pp.1-21.
https://search.emarefa.net/detail/BIM-1132928
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1132928