It is well known that the cotton aphid is the major pest in cotton fields of Northwest China, and seven-spot ladybird is an important natural enemy among the various possi- ble natural enemies of cotton aphid. In orde...It is well known that the cotton aphid is the major pest in cotton fields of Northwest China, and seven-spot ladybird is an important natural enemy among the various possi- ble natural enemies of cotton aphid. In order to increase the applications of population dynamics in integrated pest management and control the cotton aphids biologically, we need to understand the population dynamics of cotton aphid and their natural enemies. A delay predator prey system on cotton aphid and seven-spot ladybird beetle are pro- posed in this paper. Based on the comparison theorem and an iterative method, we investigate the global attra^tivity of the equilibrium points which have important bio- logical meanings. Furthermore, some numerical simulations were carried out to illustrateand expand our theoretical results, in which a conjecture to generalize the well-known Theorem 16.4 in H. R. Thiemes book was put forward, which was taken as the open problem. The numerical simulations show coexistence of periodic solution, confirming the theoretical prediction.展开更多
基金This research was supported by Startup Project of Doctor Scientific Research of Northwest A＆F University （No. Z109021414）, National Higher-Education Insti- tution General Research and Development Project （No. 2014YB023）, National Natural Science Foundation of China （No. 11461024）, the Foundation of Henan Educational Committee （No. 13B110031） and the Fundamental Research Funds for the Universities of Henan Province （No. NSFRF140139）.
文摘It is well known that the cotton aphid is the major pest in cotton fields of Northwest China, and seven-spot ladybird is an important natural enemy among the various possi- ble natural enemies of cotton aphid. In order to increase the applications of population dynamics in integrated pest management and control the cotton aphids biologically, we need to understand the population dynamics of cotton aphid and their natural enemies. A delay predator prey system on cotton aphid and seven-spot ladybird beetle are pro- posed in this paper. Based on the comparison theorem and an iterative method, we investigate the global attra^tivity of the equilibrium points which have important bio- logical meanings. Furthermore, some numerical simulations were carried out to illustrateand expand our theoretical results, in which a conjecture to generalize the well-known Theorem 16.4 in H. R. Thiemes book was put forward, which was taken as the open problem. The numerical simulations show coexistence of periodic solution, confirming the theoretical prediction.
