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 possible 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 proposed in this paper. Based on the comparison theorem and an iterative method, we investigate the global attractivity of the equilibrium points which have important biological meanings. Furthermore, some numerical simulations were carried out to illustrate and 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.
Population dynamics and stage structure in a haploid-diploid red seaweed, Gracilaria gracilis