The periodic n-species Gilpin–Ayala competition system with impulsive effect

Permanence and Periodic Solution of Predator-Prey System with Holling Type Functional Response and Impulses

“…Note that according to biological interpretation of the solutions x(t) and y(t), they must be nonnegative. Our results extend the ideas in [30]. The organization of this paper is as follows.…”

Existence and global stability of periodic solution for impulsive predator-prey model with diffusion and distributed delay

“…In this section, by using the continuation theorem of coincidence degree theory in [25][26][27][28][29][30], the existence of a periodic solution is established. We shall study the existence conditions of at least one periodic solution of system (1.3).…”

Global Positive Periodic Solutions of Generalizedn-Species Gilpin-Ayala Delayed Competition Systems with Impulses

“…. , ) is a solution of the system (9) and (10). (ii) Since ( ) = ∏ 0< < Δ ( ) is absolutely continuous on every interval ( , +1 ], ̸ = , = 1, 2, .…”

“…Now, we are at the position to study the existence of positive periodic solutions of system (9) and (10). We mainly apply the Krasnoselskii fixed-point theorem in the cone of Banach space under some conditions to prove the main Theorem 9.…”

“…Many results concerned with the permanence, global asymptotic stability, and the existence of positive periodic solutions of system (1) are obtained; we refer to [1][2][3][4][5][6][7][8][9][10] and the reference therein. However, the Lotka-Volterra type models have often been severely criticized.…”