![](/images/graphics-bg.png)
Spatiotemporal Patterns in a Ratio-Dependent Food Chain Model with Reaction-Diffusion
Author
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-17
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
Predator-prey models describe biological phenomena of pursuit-evasion interaction.
And this interaction exists widely in the world for the necessary energy supplement of species.
In this paper, we have investigated a ratio-dependent spatially extended food chain model.
Based on the bifurcation analysis (Hopf and Turing), we give the spatial pattern formation via numerical simulation, that is, the evolution process of the system near the coexistence equilibrium point (u2*,v2*,w2*), and find that the model dynamics exhibits complex pattern replication.
For fixed parameters, on increasing the control parameter c1, the sequence “holes → holes-stripe mixtures → stripes → spots-stripe mixtures → spots” pattern is observed.
And in the case of pure Hopf instability, the model exhibits chaotic wave pattern replication.
Furthermore, we consider the pattern formation in the case of which the top predator is extinct, that is, the evolution process of the system near the equilibrium point (u1*,v1*,0), and find that the model dynamics exhibits stripes-spots pattern replication.
Our results show that reaction-diffusion model is an appropriate tool for investigating fundamental mechanism of complex spatiotemporal dynamics.
It will be useful for studying the dynamic complexity of ecosystems.
American Psychological Association (APA)
Zhang, Lei. 2014. Spatiotemporal Patterns in a Ratio-Dependent Food Chain Model with Reaction-Diffusion. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1013310
Modern Language Association (MLA)
Zhang, Lei. Spatiotemporal Patterns in a Ratio-Dependent Food Chain Model with Reaction-Diffusion. Abstract and Applied Analysis No. 2014 (2014), pp.1-9.
https://search.emarefa.net/detail/BIM-1013310
American Medical Association (AMA)
Zhang, Lei. Spatiotemporal Patterns in a Ratio-Dependent Food Chain Model with Reaction-Diffusion. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1013310
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1013310