Modelling and analysis of a competitive model with stage structure

K e y w o r d s S t a g e structure, Competition, Global stability, Periodic solution. 1. I N T R O D U C T I O N The classical Lotka-Volterra type competitive system is an important population model and has been studied by many authors (see, for example, [1-9]). The two-species autonomous competitive system is of the form, ~ (t) = ~ (t) b~ ~ a~j~j (t) , i = 1, 2, (1.1) j = l where xi(t) denotes the density of the gth species at time t, respectively, bi and aij are positive constants, i , j = 1, 2. bi is the intrinsic growth rate of the ith species, aii is the intra-speeific *Author to whom all correspondence should be addressed. The authors would like to extend their appreciations to the anonymous referees for their many helpful comments and suggestions which greatly improved the presentation of this paper. The first author's work was supportd by NNSF of China (No. 10471066). 0895-7177/05/$ see front matter (~) 2005 Elsevier Ltd. All rights reserved. Typeset by .AA4S-TEX doi:10.1016/j.mcm.2004.08.003