Existence and stability of periodic solution of a stage-structured model with state-dependent impulsive effects

Abstract

A single population growth model with stage-structured and state-dependent impulsive control is proposed. By using the Poincaré map and the analogue of Poincaré's criterion, we prove the existence and the stability of positive order-1 or order-2 periodic solution. Moreover, we show that there is no periodic solution with order greater than or equal to three. Numerical results are carried out to illustrate the feasibility of our main results and the superiority of state feedback control strategy is also discussed.

Impulsive control in a stage structure population model with birth pulses

“…In our case, d = 0.1, d = 0.2, T ¼ 5 2 ln 2; p ¼ expðÀ2dTÞ ¼ From (15), b Ãà ¼ ð1þp 2 Þð3Àp 2 þp 4 þp 6 Þ p 2 þp 6 ¼ 6:9. Fig.…”

“…But different kinds of impulsive effects occur at different moments in many practical problems. Recently, authors considered different kinds of impulsive effects, which occur at different moments; see [14][15][16] for example. It is seen that these researches focused on the basic theories, such as the existence of periodic solutions and numerical simulations.…”

Impulsive predator-prey model

“…In this work, we consider a model inspired from [4] where two populations of insects denoted by x and y, respectively, are treated by chemical spray. The evolution of the two populations is governed by a predator-prey model and the effect of the chemical spray is described by impulse effects.…”

Solvability of a class of impulsive damped vibration problems

“…Impulsive differential equations arising from the real world describe the dynamics of processes in which sudden, discontinuous jumps occur. For the background, theory, and applications of impulsive differential equations, we refer the interest readers to [1][2][3][4][5][6][7][8][9]. There have been many approaches to study IPs, such as method of upper and lower solutions with the monotone iterative technique, fixed point theory, and topological degree theory.…”

“…In [28], Zhou and Li studied the existence of at least one weak solution for problem (4). They obtained the following two results.…”