Modelling and analysis of a competitive model with stage structure

A two-species Lotka-Volterra type competition model with stage structures for both species is proposed and investigated. In our model, the individuals of each species are classified as belonging either the immature or the mature. First, we consider the stage-structured model with constant coefficients. By constructing suitable Lyapunov functions, sufficient conditions are derived for the global stability of nonnegative equilibria of the proposed model. It is shown that three typical dynamical behaviors (coexistence, bistability, dominance) are possible in stage-structured competition model. Next, we consider the stage-structured competitive model in which the coefficients are assumed to be positively continuous periodic functions. By using Gaines and Mawhin's continuation theorem of coincidence degree theory, a set of easily verifiable sufficient conditions are obtained for the existence of positive periodic solutions to the model. Numerical simulations are also presented to illustrate the feasibility of our main results.