Positive periodic solutions of a class of delay differential system with feedback control

Periodic Solutions for n-Species Lotka-Volterra Competitive Systems with Pure Delays

“…In this paper, we always assume the following. From the viewpoint of mathematical biology, in this paper for system (6) we only consider the solution with the following initial conditions:…”

“…. , * ( )) be a positive periodic solution of system (6). Choose positive constants > 0, > 0 such that…”

“…For example, in [1-3, 12, 14-20], the authors studied existence of positive periodic solutions for population competition systems, in [4,5,8,13,21], the authors studied existence of positive periodic solutions for population cooperative systems, in [9], the authors studied existence of positive periodic solutions for population predator-prey system, and in [6,11], the authors studied existence of positive periodic solutions for single species systems. The continuation theorem is a powerful tool to study the existence of periodic solutions of periodic high-dimensional timedelayed problems.…”

Periodicity in predator-prey systems with multiple delays and feedback controls

“…On the other hand, recently, the study of the existence of positive periodic solutions for the population dynamical systems with feedback control and time delays have been studied extensively [14]- [24] . However, about the non-autonomous periodic Lotka-Volterra predatorprey systems with multiple time delays and feedback controls have not been fully investigated.…”

Multiple positive periodic solutions of nonlinear functional differential system with feedback control

“…However, the studies of these models with control variables are relatively few, and control variables are usually considered as constants or time dependent [5,6]. In a recent paper [7], by employing the continuation theorem of Gaines and Mawhin's coincidence degree theory [8, p. 40], the authors investigated the existence of positive periodic solutions of the following system with feedback control: dx dt = F (t, x(t − τ 1 (t)), . .…”