Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2012.2016.2025MohdMohd Hafiz HasanYahya Abu 1220121219Mathematical modelling plays an important role in the study
of prey-predator interactions. The prey-predator interactions can be modelled
by using the basic Lotka-Volterra equations, which describe the dynamics of
biological systems in which two species i.e., the prey and predator interact.
However, the presence of diffusion mechanism, changes the behaviour and nature
of the whole model. It is now a reaction-diffusion system, which takes the form
of partial differential equations and very difficult to be solved analytically.
Thus, most researchers have turned to numerical simulations so as to study the
behaviour of the system. In this study, the numerical simulations technique,
namely finite-difference method, is employed so as to study the rich spatio-temporal
dynamical structure of diffusive prey-predator model. The formations of numerous
patterns are observed i.e., spiral waves, patchy structures, spiral defect chaos
and spatio-temporal chaos due to Turing instability in our prey-predator model.
These two-dimensional patterns are in fact very beautiful and very interesting
to be observed and interpreted accordingly from the ecological point of views.]]>Murray, J.M.,19892nd Edn.,Pages: 767Pages: 767Levin, S.A., T.M. Powell and J.H. Steele,1993Pages: 307Pages: 307Malchow, H.,1993251103109Medvinsky, A.B., S.V. Petrovskii, I.A. Tikhonova, H. Malchow and B.L. Li,200244311370Holmes, E.E., M.A. Lewis, J.E. Banks, R.R. Veit,1994751729Wang, W., Q.X. Liu and Z. Jin,20072007Sherratt, J.A.,200143037Shigesada, N. and K. Kawasaki,1997Pages: 205Pages: 205Petrovskii, S.V. and H. Malchow,200159157174Garvie, M.R.,200769931956Bhattacharyay, A.,20012001Alonso, D., F. Bartumeus and J. Catalan,2002832834Sherratt, J.A., B.T. Eagan and M.A. Lewis,20073522138Wang, W., L. Zhang, H. Wang and Z. Li,2010221131140Camara, B.I. and M.A. Aziz-Alaoui,200815897906Baurmann, M., T. Gross and U. Feudel,2007245220229Dubey, B., N. Kumari and R.K. Upadhyay,200931413432