scholarly journals Periodic solutions of a discrete nonautonomous Lotka-Volterra predator-prey model with time delays

2004 ◽  
Vol 4 (3) ◽  
pp. 823-831 ◽  
Author(s):  
Rui Xu ◽  
◽  
M.A.J. Chaplain ◽  
F.A. Davidson ◽  
Keyword(s):  
Periodic Solutions ◽  
Time Delays ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Periodic solutions of a delayed predator-prey model with stage structure for predator

2004 ◽  
Vol 2004 (3) ◽  
pp. 255-270 ◽  
Author(s):  
Rui Xu ◽  
M. A. J. Chaplain ◽  
F. A. Davidson
Keyword(s):  
Periodic Solutions ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Time Dependent ◽  
Volterra Type ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Proposed Model

A periodic time-dependent Lotka-Volterra-type predator-prey model with stage structure for the predator and time delays due to negative feedback and gestation is investigated. Sufficient conditions are derived, respectively, for the existence and global stability of positive periodic solutions to the proposed 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.

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