Permanence and global stability in a discrete n-species competition system with feedback controls

Permanence of a Two Species Delayed Competitive Model With Stage Structure and Harvesting

“…For any small positive constant ε > 0, without loss of generality, we assume that ε < 1 2 m 2 , it follows from (5) and (12) that there exists a T 5 > T 3 such that (17) m 2 − ε < x 2 (t) < M 2 + ε for all t > T 5 .…”

“…Jiang [29] focused on the permanence and extinction for nonantonomous Lotka-Volterra system. For more research on the permanence behavior of predator-prey models, one can see [8,11,13,14,15,17,18,23]. Here we must point out that most of literatures on these predator-prey models are only connected with parameters which are independent of time delay, while in most applications of delay predator-prey models in population dynamics, the need of incorporation of a time delay is often the result of existence of some stage structure [1,2,9].…”

Global Attractivity and Extinction of a Discrete Competitive System with Infinite Delays and Single Feedback Control

“…In order to accurately describe such a system, scholars introduced feedback control into ecosystems. Recently, the ecosystems with feedback controls have been extensively studied and obtained many interesting results (see [12][13][14][15][16][17][18]), noting that models in [10,[12][13][14][15] considered at least two feedback controls variables, which means that, for the different species, different control strategy is adopted, whereas, in the real world, the strategy adopted for one species may also affect the other species. For example, spraying pesticide not only can reduce the number of weeds but also have a negative impact on the growth of corps or beneficial animals [19].…”

Dynamics for a discrete competition and cooperation model of two enterprises with multiple delays and feedback controls

“…Mukherjee [2] addressed the permanence and global attractivity for facultative mutualism predator-prey model, Zhao and Jiang [3] considered the permanence and extinction for Lotka-Volterra model, Teng et al [4] established the permanence criteria for a delayed discrete species systems, Liu et al [5] studied the permanence and periodic solutions for reaction-diffusion food-chain system with impulsive effect. For more detailed research about this topic, one can see [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In real life, the co-existence and stability of enterprise clusters has become one of the most prevalent phenomena in our society.…”