Permanence and global attractivity in a discrete Lotka-Volterra predator-prey model with delays

Abstract

In this paper, we deal with a discrete Lotka-Volterra predator-prey model with time-varying delays. For the general non-autonomous case, sufficient conditions which ensure the permanence and global stability of the system are obtained by using differential inequality theory. For the periodic case, sufficient conditions which guarantee the existence of a unique globally stable positive periodic solution are established. The paper ends with some interesting numerical simulations that illustrate our analytical predictions. MSC: 34K20; 34C25; 92D25

Dynamics of a Discrete Allelopathic Phytoplankton Model with Infinite Delays and Feedback Controls

“…As we all know, due to seasonal fluctuations in the environment and hereditary factors, time delays have been introduced into the biological system (see [11,14,21,[27][28][29][30][31][32][33][34][35][36]). Zhao et al [8] further considered a discrete Lotka-Volterra competition system with infinite delays and single feedback control variable as follows:…”

Robust QLM-SCFTK matrix approach applied to a biological population model of fractional order considering the carrying capacity

“…In [32], the author studied the asymptotic spreading of a LV predator-prey model with self-limit effect. A discrete LV predator-prey system with variable time delays was considered in [46] and the global stability of the model obtained via the differential inequality theory. In [50], a standard LV predator-prey system with white noise was studied and its ergoric property under a higher order perturbation of white noise and regime switching was examined.…”