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Discrete models and Fisher's maximum principle in ecology
1.  Department of Technology, University of Kalmar, S39182 Kalmar, Sweden 
[1] 
Xiaoli Liu, Dongmei Xiao. Bifurcations in a discrete time LotkaVolterra predatorprey system. Discrete & Continuous Dynamical Systems  B, 2006, 6 (3) : 559572. doi: 10.3934/dcdsb.2006.6.559 
[2] 
Rui Xu, M.A.J. Chaplain, F.A. Davidson. Periodic solutions of a discrete nonautonomous LotkaVolterra predatorprey model with time delays. Discrete & Continuous Dynamical Systems  B, 2004, 4 (3) : 823831. doi: 10.3934/dcdsb.2004.4.823 
[3] 
Qizhen Xiao, Binxiang Dai. Heteroclinic bifurcation for a general predatorprey model with Allee effect and state feedback impulsive control strategy. Mathematical Biosciences & Engineering, 2015, 12 (5) : 10651081. doi: 10.3934/mbe.2015.12.1065 
[4] 
Christian Kuehn, Thilo Gross. Nonlocal generalized models of predatorprey systems. Discrete & Continuous Dynamical Systems  B, 2013, 18 (3) : 693720. doi: 10.3934/dcdsb.2013.18.693 
[5] 
Meng Fan, Qian Wang. Periodic solutions of a class of nonautonomous discrete time semiratiodependent predatorprey systems. Discrete & Continuous Dynamical Systems  B, 2004, 4 (3) : 563574. doi: 10.3934/dcdsb.2004.4.563 
[6] 
JingAn Cui, Xinyu Song. Permanence of predatorprey system with stage structure. Discrete & Continuous Dynamical Systems  B, 2004, 4 (3) : 547554. doi: 10.3934/dcdsb.2004.4.547 
[7] 
Dongmei Xiao, Kate Fang Zhang. Multiple bifurcations of a predatorprey system. Discrete & Continuous Dynamical Systems  B, 2007, 8 (2) : 417433. doi: 10.3934/dcdsb.2007.8.417 
[8] 
Peng Feng. On a diffusive predatorprey model with nonlinear harvesting. Mathematical Biosciences & Engineering, 2014, 11 (4) : 807821. doi: 10.3934/mbe.2014.11.807 
[9] 
Ronald E. Mickens. Analysis of a new class of predatorprey model. Conference Publications, 2001, 2001 (Special) : 265269. doi: 10.3934/proc.2001.2001.265 
[10] 
Mostafa Fazly, Mahmoud Hesaaraki. Periodic solutions for a semiratiodependent predatorprey dynamical system with a class of functional responses on time scales. Discrete & Continuous Dynamical Systems  B, 2008, 9 (2) : 267279. doi: 10.3934/dcdsb.2008.9.267 
[11] 
Yun Kang, Sourav Kumar Sasmal, Amiya Ranjan Bhowmick, Joydev Chattopadhyay. Dynamics of a predatorprey system with prey subject to Allee effects and disease. Mathematical Biosciences & Engineering, 2014, 11 (4) : 877918. doi: 10.3934/mbe.2014.11.877 
[12] 
Xinyu Song, Liming Cai, U. Neumann. Ratiodependent predatorprey system with stage structure for prey. Discrete & Continuous Dynamical Systems  B, 2004, 4 (3) : 747758. doi: 10.3934/dcdsb.2004.4.747 
[13] 
Miljana JovanoviĆ, Marija KrstiĆ. Extinction in stochastic predatorprey population model with Allee effect on prey. Discrete & Continuous Dynamical Systems  B, 2017, 22 (7) : 26512667. doi: 10.3934/dcdsb.2017129 
[14] 
Xiaoling Li, Guangping Hu, Zhaosheng Feng, Dongliang Li. A periodic and diffusive predatorprey model with disease in the prey. Discrete & Continuous Dynamical Systems  S, 2017, 10 (3) : 445461. doi: 10.3934/dcdss.2017021 
[15] 
Yang Lu, Xia Wang, Shengqiang Liu. A nonautonomous predatorprey model with infected prey. Discrete & Continuous Dynamical Systems  B, 2018, 23 (9) : 38173836. doi: 10.3934/dcdsb.2018082 
[16] 
Zaidong Zhan, Shuping Chen, Wei Wei. A unified theory of maximum principle for continuous and discrete time optimal control problems. Mathematical Control & Related Fields, 2012, 2 (2) : 195215. doi: 10.3934/mcrf.2012.2.195 
[17] 
Benjamin Leard, Catherine Lewis, Jorge Rebaza. Dynamics of ratiodependent PredatorPrey models with nonconstant harvesting. Discrete & Continuous Dynamical Systems  S, 2008, 1 (2) : 303315. doi: 10.3934/dcdss.2008.1.303 
[18] 
Wei Feng, Michael T. Cowen, Xin Lu. Coexistence and asymptotic stability in stagestructured predatorprey models. Mathematical Biosciences & Engineering, 2014, 11 (4) : 823839. doi: 10.3934/mbe.2014.11.823 
[19] 
WanTong Li, YongHong Fan. Periodic solutions in a delayed predatorprey models with nonmonotonic functional response. Discrete & Continuous Dynamical Systems  B, 2007, 8 (1) : 175185. doi: 10.3934/dcdsb.2007.8.175 
[20] 
Guirong Jiang, Qishao Lu. The dynamics of a PreyPredator model with impulsive state feedback control. Discrete & Continuous Dynamical Systems  B, 2006, 6 (6) : 13011320. doi: 10.3934/dcdsb.2006.6.1301 
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