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Báo cáo hoa học: " Research Article Almost Periodic Solutions of Prey-Predator Discrete Models with Delay"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Almost Periodic Solutions of Prey-Predator Discrete Models with Delay | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 976865 19 pages doi 10.1155 2009 976865 Research Article Almost Periodic Solutions of Prey-Predator Discrete Models with Delay Tomomi Itokazu and Yoshihiro Hamaya Department of Information Science Okayama University of Science 1-1 Ridai-cho Okayama 700-0005 Japan Correspondence should be addressed to Yoshihiro Hamaya hamaya@mis.ous.ac.jp Received 10 February 2009 Revised 18 May 2009 Accepted 9 July 2009 Recommended by Elena Braverman The purpose of this article is to investigate the existence of almost periodic solutions of a system of almost periodic Lotka-Volterra difference equations which are a prey-predator system x1 n 1 X1 n exp b1 n -a1 n x1 n -c2 n 2s -OT K2 n-s x2 s x2 n 1 x2 n exp -b2 n -a2 n x2 n c1 n ffs - K1 n - s x1 s and a competitive system xfn 1 xfn exp bj n -anxfn - jj i Zn - Kj n - s xj s by using certain stability properties which are referred to as K p -weakly uniformly asymptotic stable in hull and K p -totally stable. Copyright 2009 T. Itokazu and Y. Hamaya. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction and Preliminary For ordinary differential equations and functional differential equations the existence of almost periodic solutions of almost periodic systems has been studied by many authors. One of the most popular methods is to assume the certain stability properties 1-4 . Recently Song and Tian 5 have shown the existence of periodic and almost periodic solutions for nonlinear Volterra difference equations by means of K p -stability conditions. Their results are to extend results in Hamaya 2 to discrete Volterra equations. To the best of our knowledge there are no relevant results on almost periodic solutions for discrete Lotka-Volterra models by means of our approach except .