Periodic solutions of a class of nonautonomous discrete time semi-ratio-dependent predator-prey systems

Previous Article
A monotone-iterative method for finding periodic solutions of an impulsive competition system on tumor-normal cell interaction
DCDS-B Home
This Issue
Next Article
The dynamics of public goods

August 2004, 4(3): 563-574. doi: 10.3934/dcdsb.2004.4.563

Periodic solutions of a class of nonautonomous discrete time semi-ratio-dependent predator-prey systems

1.	School of Mathematics and Statistics, and Key Laboratory for Vegetation Ecology of the Education Ministry, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, China
2.	Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alta., Canada T6G 2G1, Canada

Received February 2003 Revised December 2003 Published May 2004

Abstract
Related Papers

In this paper, we establish sufficient criteria for the existence of positive periodic solutions for a class of discrete time semi-ratio-dependent predator-prey interaction models based on systems of nonautonomous difference equations. The approach involves the coincidence degree and its related continuation theorem as well as some priori estimates.

Keywords: periodic solutions, coincidence degree., difference equations, Predator-prey systems, semiratio-dependent.

Mathematics Subject Classification: 39A11, 39A12, 92D2.

Citation: Meng Fan, Qian Wang. Periodic solutions of a class of nonautonomous discrete time semi-ratio-dependent predator-prey systems. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 563-574. doi: 10.3934/dcdsb.2004.4.563

[1]	Mostafa Fazly, Mahmoud Hesaaraki. Periodic solutions for a semi-ratio-dependent predator-prey dynamical system with a class of functional responses on time scales. Discrete & Continuous Dynamical Systems - B, 2008, 9 (2) : 267-279. doi: 10.3934/dcdsb.2008.9.267
[2]	Zhicheng Wang, Jun Wu. Existence of positive periodic solutions for delayed ratio-dependent predator-prey system with stocking. Communications on Pure & Applied Analysis, 2006, 5 (3) : 423-433. doi: 10.3934/cpaa.2006.5.423
[3]	Wan-Tong Li, Yong-Hong Fan. Periodic solutions in a delayed predator-prey models with nonmonotonic functional response. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 175-185. doi: 10.3934/dcdsb.2007.8.175
[4]	Xinyu Song, Liming Cai, U. Neumann. Ratio-dependent predator-prey system with stage structure for prey. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 747-758. doi: 10.3934/dcdsb.2004.4.747
[5]	Fei Xu, Ross Cressman, Vlastimil Křivan. Evolution of mobility in predator-prey systems. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3397-3432. doi: 10.3934/dcdsb.2014.19.3397
[6]	Christian Kuehn, Thilo Gross. Nonlocal generalized models of predator-prey systems. Discrete & Continuous Dynamical Systems - B, 2013, 18 (3) : 693-720. doi: 10.3934/dcdsb.2013.18.693
[7]	Guanqi Liu, Yuwen Wang. Stochastic spatiotemporal diffusive predator-prey systems. Communications on Pure & Applied Analysis, 2018, 17 (1) : 67-84. doi: 10.3934/cpaa.2018005
[8]	Xiaoling Li, Guangping Hu, Zhaosheng Feng, Dongliang Li. A periodic and diffusive predator-prey model with disease in the prey. Discrete & Continuous Dynamical Systems - S, 2017, 10 (3) : 445-461. doi: 10.3934/dcdss.2017021
[9]	Rui Xu, M.A.J. Chaplain, F.A. Davidson. Periodic solutions of a discrete nonautonomous Lotka-Volterra predator-prey model with time delays. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 823-831. doi: 10.3934/dcdsb.2004.4.823
[10]	Zhijun Liu, Weidong Wang. Persistence and periodic solutions of a nonautonomous predator-prey diffusion with Holling III functional response and continuous delay. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 653-662. doi: 10.3934/dcdsb.2004.4.653
[11]	Benjamin Leard, Catherine Lewis, Jorge Rebaza. Dynamics of ratio-dependent Predator-Prey models with nonconstant harvesting. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 303-315. doi: 10.3934/dcdss.2008.1.303
[12]	Canan Çelik. Dynamical behavior of a ratio dependent predator-prey system with distributed delay. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 719-738. doi: 10.3934/dcdsb.2011.16.719
[13]	Antoni Leon Dawidowicz, Anna Poskrobko. Stability problem for the age-dependent predator-prey model. Evolution Equations & Control Theory, 2018, 7 (1) : 79-93. doi: 10.3934/eect.2018005
[14]	Marcos Lizana, Julio Marín. On the dynamics of a ratio dependent Predator-Prey system with diffusion and delay. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1321-1338. doi: 10.3934/dcdsb.2006.6.1321
[15]	Hanwu Liu, Lin Wang, Fengqin Zhang, Qiuying Li, Huakun Zhou. Dynamics of a predator-prey model with state-dependent carrying capacity. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 1-15. doi: 10.3934/dcdsb.2019028
[16]	Shanshan Chen, Jianshe Yu. Stability and bifurcation on predator-prey systems with nonlocal prey competition. Discrete & Continuous Dynamical Systems - A, 2018, 38 (1) : 43-62. doi: 10.3934/dcds.2018002
[17]	Xinjian Wang, Guo Lin. Asymptotic spreading for a time-periodic predator-prey system. Communications on Pure & Applied Analysis, 2019, 18 (6) : 2983-2999. doi: 10.3934/cpaa.2019133
[18]	Zengji Du, Xiao Chen, Zhaosheng Feng. Multiple positive periodic solutions to a predator-prey model with Leslie-Gower Holling-type II functional response and harvesting terms. Discrete & Continuous Dynamical Systems - S, 2014, 7 (6) : 1203-1214. doi: 10.3934/dcdss.2014.7.1203
[19]	Juan C. Jara, Felipe Rivero. Asymptotic behaviour for prey-predator systems and logistic equations with unbounded time-dependent coefficients. Discrete & Continuous Dynamical Systems - A, 2014, 34 (10) : 4127-4137. doi: 10.3934/dcds.2014.34.4127
[20]	Inkyung Ahn, Wonlyul Ko, Kimun Ryu. Asymptotic behavior of a ratio-dependent predator-prey system with disease in the prey. Conference Publications, 2013, 2013 (special) : 11-19. doi: 10.3934/proc.2013.2013.11

2017 Impact Factor: 0.972

American Institute of Mathematical Sciences