Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation Delays

Abstract

We investigate a nonautonomous two-species competitive system with stage structure and double time delays due to maturation for two species, where toxic effect of toxin liberating species on nontoxic species is considered and the inhibiting effect is zero in absence of either species. Positivity and boundedness of solutions are analytically studied. By utilizing some comparison arguments, an iterative technique is proposed to discuss permanence of the species within competitive system. Furthermore, existence of positive periodic solutions is investigated based on continuation theorem of coincidence degree theory. By constructing an appropriate Lyapunov functional, sufficient conditions for global stability of the unique positive periodic solution are analyzed. Numerical simulations are carried out to show consistency with theoretical analysis.

Extinction of a two species non-autonomous competitive system with Beddington-DeAngelis functional response and the effect of toxic substances

“…For more work on competitive system with toxic substance, one could refer to [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][35][36][37][38] and the references cited therein. On the other hand, based on the traditional Lotka-Volterra competition model, some scholars argued that the more appropriate competition model should with nonlinear inter-inhibition terms.…”

Extinction in Two-Species Nonlinear Discrete Competitive System

“…As we all know, the competitive system has been established and was accepted by many scientists and now it became the most important means to explain the ecological phenomenon. During the last decade, the study of the dynamic behaviors of competitive system with toxic substance or feedback control have been discussed by many authors; see, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. However, most of the studies are based on the traditional Lotka-Volterra competitive system [5,7,8,[17][18][19][20]; seldom did scholars consider the nonlinear case [1-4, 8, 9, 11, 12, 15, 16, 21-25].…”