scholarly journals Multiple positive periodic solutions of a Gause-type predator-prey model with Allee effect and functional responses

2020 ◽  
Vol 5 (6) ◽  
pp. 6135-6148 ◽  
Author(s):  
Shanshan Yu ◽  
◽  
Jiang Liu ◽  
Xiaojie Lin ◽  
Keyword(s):  
Periodic Solutions ◽  
Allee Effect ◽  
Positive Periodic Solutions ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Existence and Uniqueness of Positive Periodic Solutions for a Delayed Predator-Prey Model with Dispersion and Impulses

2014 ◽  
Vol 2014 ◽  
pp. 1-21
Author(s):  
Zhenguo Luo ◽  
Liping Luo ◽  
Liu Yang ◽  
Zhenghui Gao ◽  
Yunhui Zeng
Keyword(s):  
Periodic Solutions ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Predator Population ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

An impulsive Lotka-Volterra type predator-prey model with prey dispersal in two-patch environments and time delays is investigated, where we assume the model of patches with a barrier only as far as the prey population is concerned, whereas the predator population has no barriers between patches. By applying the continuation theorem of coincidence degree theory and by means of a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are obtained to guarantee the existence, uniqueness, and global stability of positive periodic solutions of the system. Some known results subject to the underlying systems without impulses are improved and generalized. As an application, we also give two examples to illustrate the feasibility of our main results.

scholarly journals Positive Periodic Solutions of a Neutral Impulsive Predator-Prey Model

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Guirong Liu ◽  
Xiaojuan Song
Keyword(s):  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Impulsive System ◽  
Impulsive Effect ◽  
Neutral System ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

We investigate a ratio-dependent predator-prey model with Holling type III functional response based on system of neutral impulsive differential equations. Sufficient conditions for existence of positive periodic solutions are obtained by applying continuation theorem. Our main results demonstrate that under the suitable periodic impulse perturbations, the neutral impulsive system preserves the periodicity of the corresponding neutral system without impulse. In addition, our results can be applied to the corresponding system without impulsive effect, and thus, extend previous results.

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