The dynamics of an impulsive delay predator–prey model with stage structure and Beddington-type functional response

Analysis of a predator-prey system with Beddington-type functional response and stage-structure of prey

“…In recent years, Huang, Li and Huo (2012), Fu, Zhang and Hu (2013) and She and Li (2013) analysed some stage-structured models of population growth with immature and mature individuals, where the stage-structure was modelled by using a constant time delay. Just as Chen, Xie and Li (2012), Shao and Dai (2010) and Hasan and Hama (2012) pointed out that the delay differential equation exhibited much complicated dynamics, since a time delay could cause the population to fluctuate and cause a stable equilibrium to become unstable, and so on. Moreover, considering environmental damage from spreading pesticides, in order to minimise biological damage, in real world, only using biological method to control pests was being paid more and more attention, Kar and Ghosh (2012), Prasad, Banerjee and Srinivasu (2013) Terry (2014) and many other authors have studied hardly on this.…”

Dynamic of a delayed predator–prey model with birth pulse and impulsive harvesting in a polluted environment

“…And these papers get the theoretical threshold value for the persistence or extinction of the population. There are a lot of works on predator-prey models [8][9][10][11][12][13][14]. As a matter of fact, the prey preyed on by the predator cannot be translated immediately into offspring of predator population in the natural environment.…”

Analysis of an Impulsive One-Predator and Two-Prey System with Stage-Structure and Generalized Functional Response

“…On the other hand, for predator-prey model, in description of the relationship between predator and prey, a crucial element is the classic definition of a predator's functional response. Recently, the dynamics of predator-prey systems with different kinds of functional responses have been studied in relevant literature, such as Holling type [6], Crowley-Martin type [7][8][9], Beddington-DeAngelis type [10,11], Watt type [12,13], and Ivlev type [14]. For example, Gakkhar and Naji [15] investigated the dynamical behaviors of the following threespecies system with nonlinear functional response: …”