One of the central issues in ecology is the study of spatial pattern in the distribution of organisms. Thus, in this paper, spatial pattern of a predatorprey system with predator cannibalism is considered. By mathematical analysis, we obtain the condition for emerging Turing pattern formation. Furthermore, numerical simulations reveal that large variety of different spatiotemporal dynamics emerge as the consequence of the interaction of Holling type II with predator cannibalism. The obtained results show predator cannibalism has great influence on the spatial pattern formation. In other words, the regular pattern is induced by predator cannibalism. Moreover, we find that although the environment is heterogeneous, the system still exhibits Turing pattern, which means the pattern is self-organized. It may help us better understand the

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In this paper, the existence of solutions for a system of nonlinear equations is considered. 2 n nonzero real solutions are obtained by using the critical point theory. Additionally, the Dirichlet boundary value problems of even order difference equations and partial difference equations are investigated.  2005 Elsevier Inc. All rights reserved.