Chaotic behavior of a chemostat model with Beddington–DeAngelis functional response and periodically impulsive invasion

The dynamic complexity of an impulsive Holling II predator–prey model with mutual interference

“…Based on many experiments, Holling [7] suggested three different kinds of functional response for different kinds of species, which made the standard Lotka-Volterra systems more realistic. Many researchers studied different functional responses such as Lotka-Volterra responses [8], Holling-type [9][10][11][12] and Bedington-type [13][14][15]. The predator-prey system with impulsive [16,17] effects has been introduced and studied by many researchers (see, for instance [18][19][20][21][22] and the references therein).…”

The reverse effects of random perturbation on discrete systems for single and multiple population models

“…Recently, the interaction between multiple species and discrete host-parasitoid models have been proposed and studied. In particular, different functional response functions have been involved into the classical host-parasitoid model, such as Lotka-Volterra model [19] , Hollingtype functional response functions [20][21][22] and Bedington-type functional response function [23][24][25] . For example, Tang and Chen [26] developed two host-parasitoid models with Holling type II and III functional response functions, respectively, and the complex dynamics have been investigated in more detail by using numerical bifurcation analyses.…”

Stability and Bifurcation Analysis for a Predator-Prey Model with Discrete and Distributed Delay

“…Therefore, a more realistic predator-prey model should be described by delayed differential equations (DDEs) [3][4][5][6][7][8][9][10][11]. In general, delay differential equations exhibit more complicated dynamics on stability, periodic structure, bifurcation, and so on [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. In [27,28], the authors investigated the effect of the discrete delay on the stability of the model.…”