Permanence and stability of an Ivlev-type predator–prey system with impulsive control strategies

Complex behavior in an Ivlev-type mutual interference predator-prey model concerning IPM

“…Let T = (n 2 + n 3 )T . Then, there exist a t 2 ∈ [(n 1 +1)T, (n 1 +1)T +T ] such that x(t 2 ) > m 3 . Otherwise x(t) < m 3 , t 2 ∈ [(n 1 + 1)T, (n 1 + 1)T + T ].…”

“…Ivlev [1] gave a nonmonotonic functional response with φ(x) = 1 − e −cx (t) , where c is a positive parameter. Recently, an Ivlev-type predator-prey system with impulsive effect studied in [2], [3], [4]. They proved that there exists a locally stable pest eradication periodic solution when the impulsive period is less than certain critical values; otherwise, the system is permanent.…”

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

“…In the modeling process, these perturbations are often assumed to be in the form of impulses. Based on traditional models, impulsive differential equations are proposed and extensively used in some applied fields, especially in population dynamics; see 2 Discrete Dynamics in Nature and Society [17][18][19]. The theory of impulsive differential equation is now being recognized richer than the corresponding differential equation without impulses, which plays a key role in the development of biomathematics; see monographs [20,21] and references cited therein.…”

The dynamics of a delayed Gompertz model with Holling IV function response and impulsive effects at different moment on the prey

“…For example, Wang [12] proposed a stage-structured predatorprey system with impulsive stocking immature prey and harvesting predator at different moment. Baek [13] considered impulsive control strategies containing a biological control and a chemical control with the same period, but not simultaneously. Their study shows that twice impulses at different moment bring different effects on the dynamics, see references [12][13][14].…”

“…Baek [13] considered impulsive control strategies containing a biological control and a chemical control with the same period, but not simultaneously. Their study shows that twice impulses at different moment bring different effects on the dynamics, see references [12][13][14]. Recently, pulses are even introduced into delayed predator-prey by many researchers [15][16][17].…”