Complex dynamics of Holling type II Lotka–Volterra predator–prey system with impulsive perturbations on the predator ☆

By Xianning Liu, Lansun Chen. 2003

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Impulsive state feedback control of a predator-prey model (2007, background): “For example, in impulsive vaccination of disease models (see [5,13,15]) and population models (see [3,10,11,14,17]), the properties of their solutions are discussed under the conditions that the impulses occur at fixed moments t = tk or even periodic fixed moments t = nT .”
An integrated pest management model with delayed responses to pesticide applications and its threshold dynamics (2012, background): “Here a system is said to be permanent if for a large enough t there exists a region D, such that any solution of this system enters and remains in D [58].”
A predator-prey model with disease in the prey and two impulses for integrated pest management (2009, methodology): “Impulsive equations [20,21] have been recently used in population dynamics in relation to impulsive vaccination [22], population ecology [23,24], the chemotherapeutic treatment of disease [25], the theory of the chemostat [26].”