Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2012.2252.2258MohdMohd HafizHasanYahya Abu1220121221The aim of this study was to predict the large time behaviour
of solutions of diffusive prey-predator model, by using the notions of invariant
region, energy estimates and exponential stability. The exponential stability
was measured in terms of energy; defined by the square of L^{2}-norm
of solutions. By first constructing and proving the invariant region of the
model, the occurrence of energy decaying exponentially in the long run was shown
by using classical energy method. The interpretation and significance of such
decay was discussed and some numerical evidences are presented so as to support
the theoretical results.]]>Kaipio, J.P., J. Tervo and M. Vauhkonen,1995Dunn, J.M., T.D. Wentzel, S. Schreider and L. McArthur,2009Murray, J.M.,1989Levin, S.A., T.M. Powell and J.H. Steele,1993Malchow, H.,1993Medvinsky, A.B., S.V. Petrovskii, I.A. Tikhonova, H. Malchow and B.L. Li,2002Holmes, E.E., M.A. Lewis, J.E. Banks, R.R. Veit,1994Smoller, J.,1992Logan, J.D.,2008Tveito, A. and R. Winther,2005Britton, N.F.,1986Korman, P.,1990Raposo, C.A., M. Sepulveda, O.V. Villagran, D.C. Pereira and M.L. Santos,2008Gopalsamy, K.,1977Chueh, K., C. Conley and J. Smoller,1977Wang, W., Q.X. Liu and Z. Jin,2007