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Research articles

ScienceAsia 39S(2013): 31-36 |doi: 10.2306/scienceasia1513-1874.2013.39S.031


Modelling the spatiotemporal dynamics of diffusive prey-predator interactions: Pattern formation and ecological implications


Mohd Hafiz Mohda,b,*, Yahya Abu Hasana

 
ABSTRACT:     In this paper, we investigate the formation of spatiotemporal patterns in ecological systems via numerical simulations. We study the diffusive prey-predator model and observe the rich dynamical structure as a result of prey-predator interactions in one and two spatial dimensions. In 1-d numerical investigations we show that, for a large class of initial conditions, the evolution of the model leads to the emergence of non-stationary irregular patterns, given that the local kinetics of the system is oscillatory. This corresponds to spatiotemporal chaos. The irregular patterns first emerge inside a subdomain of the system. This subdomain then steadily grows with time and, finally, the irregular chaotic patterns invade the whole space, displacing the regular pattern. For 2-d numerical simulations we observed the formation of spiral waves, patchy structures, spiral defect chaos and spatiotemporal chaos due to Turing instability in our prey-predator model. These two-dimensional patterns are very beautiful and very interesting to be observed and interpreted from the ecological point of view.

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a School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
b Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand

* Corresponding author, E-mail: mohdhafizmohd@gmail.com

Received 7 Jan 2013, Accepted 5 Apr 2013