Extinction and permanence in competitive stage structured system with time-delays

Travelling wave and convergence in stage-structured reaction–diffusion competitive models with nonlocal delays

“…Moreover, they are often much simpler than the corresponding models governed by partial differential equations. There has been much work on modelling stage-structured population models (see, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][18][19][20][21][22]24,25]). In [1], the work of Aiello and Freedman on a single species growth model with stage structure, represents a mathematically careful and biologically meaningful approach.…”

Permanence extinction and global asymptotic stability in a stage structured system with distributed delays

“…This model was extended in [15] to n-competing species where only mature species can compete with themselves for the common resource, so the competition with the immature species can be ignored. They proved that the system with stage-structure has similar behavior to that without stage-structure.…”

“…Mathematically speaking, to model the fluctuation of the environment it is assumed that the coefficients of the system are functions of time (see [11]). In this regard, Liu et al considered in [16] the nonautonomous version of their autonomous competitive system in [15], i.e., for i = 1, . .…”

“…Later, Gopalsamy and He [23] point out that in several cases of animal populations, the past dietary and nutritional history of an animal over a long period plays an influential role in determining the current behavior of the animals and in such cases distributed time delays will be appropriate. We note that in the previous studied stage-structured systems (see, for instance, [14][15][16]), delayed feedback responses in competition among the mature species are ignored. Motivated by the works on competitive Lotka-Volterra systems with distributed delays (see [7,9,10,12,19]), it is our goal here in this paper to introduce distributed delay terms into the n-species nonautonomous competitive stage-structured system (1.3).…”

Bifurcations and Control in a Singular Biological Economic Model

“…In the following decades, much research efforts are put into the investigation of biological dynamical systems with stage structure for population. Some related research results can be found in [1,2,3,10,14,26,8,39,34,35,36,37,38,40,44,41,42,43,45,47,51,52,54,25,16,9] and the references therein.Recently, the dynamics of a class of stage-structured prey-predator models with discrete time delay have been studied by several authors [4,55,18,58,5] and the references therein.Arino et al [4] suggested that the time delay to adulthood should be state dependent and careful formulation of such state dependent time delays can lead to models that produce periodic solutions. Xu et al [55] studied the persistence and stability of a delayed prey-predator model with stage structure for predator.…”