Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with Diffusion

Joint Authors

Jung, Dong Ick
Baek, Hunki
Wang, Zhi-wen

Source

Discrete Dynamics in Nature and Society

Issue

Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-14, 14 p.

Publisher

Hindawi Publishing Corporation

Publication Date

2013-04-04

Country of Publication

Egypt

No. of Pages

14

Main Subjects

Mathematics

Abstract EN

We investigate spatiotemporal dynamics of a semi-ratio-dependent predator-prey system with reaction-diffusion and zero-flux boundary.

We obtain the conditions for Hopf, Turing, and wave bifurcations of the system in a spatial domain by making use of the linear stability analysis and the bifurcation analysis.

In addition, for an initial condition which is a small amplitude random perturbation around the steady state, we classify spatial pattern formations of the system by using numerical simulations.

The results of numerical simulations unveil that there are various spatiotemporal patterns including typical Turing patterns such as spotted, spot-stripelike mixtures and stripelike patterns thanks to the Turing instability, that an oscillatory wave pattern can be emerged due to the Hopf and wave instability, and that cooperations of Turing and Hopf instabilities can cause occurrence of spiral patterns instead of typical Turing patterns.

Finally, we discuss spatiotemporal dynamics of the system for several different asymmetric initial conditions via numerical simulations.

American Psychological Association (APA)

Baek, Hunki& Jung, Dong Ick& Wang, Zhi-wen. 2013. Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with Diffusion. Discrete Dynamics in Nature and Society،Vol. 2013, no. 2013, pp.1-14.
https://search.emarefa.net/detail/BIM-488783

Modern Language Association (MLA)

Baek, Hunki…[et al.]. Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with Diffusion. Discrete Dynamics in Nature and Society No. 2013 (2013), pp.1-14.
https://search.emarefa.net/detail/BIM-488783

American Medical Association (AMA)

Baek, Hunki& Jung, Dong Ick& Wang, Zhi-wen. Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with Diffusion. Discrete Dynamics in Nature and Society. 2013. Vol. 2013, no. 2013, pp.1-14.
https://search.emarefa.net/detail/BIM-488783

Data Type

Journal Articles

Language

English

Notes

Includes bibliographical references

Record ID

BIM-488783