重庆师范大学学报（自然科学版）
重慶師範大學學報（自然科學版）
중경사범대학학보（자연과학판）
JOURNAL OF CHONGQING NORMAL UNIVERSITY（NATURAL SCIENCE EDITION）
2012年
1期
49-55
,共7页
离散互惠系统%时滞%迭合度%周期解
離散互惠繫統%時滯%迭閤度%週期解
리산호혜계통%시체%질합도%주기해
discrete mutual system%time delay%coincidence degree%periodic solution
本文研究了一类散互惠系统{x(k+ 1) =x(k)exp[r1(k)(1 -x(k-(T)(k))/k1(k)) +a(k)y(k)] y(k + 1) y(k)exp[r2(k)(1 _y(k -(T)(k))/k2(k)) +b(k)x(k)],运用迭合度和与其相关的连续性定理及先验估计,得到了系统存在正周期解的易于验证的充分条件,也就是,若下列条件i)ri(i=1,2),k(j)(j=1,2),a,b:Z→R+是ω周期的；ii)a‘＞(r1/k1)M,bL＞(r2/k2)M；iii)rL1＞aMKM1满足,则系统至少有一个正的ω周期解,所得结果是前人工作的重要的补充.
本文研究瞭一類散互惠繫統{x(k+ 1) =x(k)exp[r1(k)(1 -x(k-(T)(k))/k1(k)) +a(k)y(k)] y(k + 1) y(k)exp[r2(k)(1 _y(k -(T)(k))/k2(k)) +b(k)x(k)],運用迭閤度和與其相關的連續性定理及先驗估計,得到瞭繫統存在正週期解的易于驗證的充分條件,也就是,若下列條件i)ri(i=1,2),k(j)(j=1,2),a,b:Z→R+是ω週期的；ii)a‘＞(r1/k1)M,bL＞(r2/k2)M；iii)rL1＞aMKM1滿足,則繫統至少有一箇正的ω週期解,所得結果是前人工作的重要的補充.
본문연구료일류산호혜계통{x(k+ 1) =x(k)exp[r1(k)(1 -x(k-(T)(k))/k1(k)) +a(k)y(k)] y(k + 1) y(k)exp[r2(k)(1 _y(k -(T)(k))/k2(k)) +b(k)x(k)],운용질합도화여기상관적련속성정리급선험고계,득도료계통존재정주기해적역우험증적충분조건,야취시,약하렬조건i)ri(i=1,2),k(j)(j=1,2),a,b:Z→R+시ω주기적；ii)a‘＞(r1/k1)M,bL＞(r2/k2)M；iii)rL1＞aMKM1만족,칙계통지소유일개정적ω주기해,소득결과시전인공작적중요적보충.
In this paper,a discrete-time mutual system{x(k+ 1) =x(k)exp[r1(k)(1 -x(k-(T)(k))/k1(k)) +a(k)y(k)] y(k + 1) y(k)exp[r2(k)(1 _y(k -(T)(k))/k2(k)) +b(k)x(k)],is considered.By using coincidence degree and the related continuation the orem as well as prior estimates,easily verifiable sufficient conditions for the existence of positive periodic solutions are obtained,i.e.,if the following conditions i) ri (i =1,2),kj(j =1,2),a,b:Z→R+ areω periodic;ii) aL ＞ (r1/k1)M,bL＞( r2/k2)M;iii)(r)L1＞aMkM1 hold,then system has at least an ω periodic solution.Our results are important complement to earlier results in the literature.
