ALMOST SUFFICIENT AND NECESSARY CONDITIONS FOR PERMANENCE AND EXTINCTION OF NONAUTONOMOUS DISCRETE LOGISTIC SYSTEMS WITH TIME-VARYING DELAYS AND FEEDBACK CONTROL

作者：Xu Jiabo^*; Teng Zhidong; Gao Shujing

来源：Applications of Mathematics, 2011, 56(2): 207-225.

DOI：10.1007/s10492-011-0003-6

• discrete system
• permanence
• extinction
• feedback control
• time-varying delay

A class of nonautonomous discrete logistic single-species systems with time varying pure-delays and feedback control is studied. By introducing a new research method, almost sufficient and necessary conditions for the permanence and extinction of species are obtained. Particularly, when the system degenerates into a periodic system, sufficient and necessary conditions on the permanence and extinction of species are obtained. Moreover, a very important fact is found in our results, that is, the feedback control and delays are harmless for the permanence and extinction of species for discrete single-species systems. This shows that in a discrete single-species system introducing the feedback control to factitiously control the permanence and extinction of species is useles.

• 出版日期2011-4
• 单位赣南师范大学; 新疆大学