September  2009, 12(2): 495-510. doi: 10.3934/dcdsb.2009.12.495

A metapopulation model with local competitions

1. 

Department of Mathematics, Southern Illinois University, Carbondale, IL 62901, United States

2. 

Department of Mathematics, Purdue University, West Lafayette, IN 47907-1395

Received  September 2008 Revised  April 2009 Published  July 2009

A metapopulation model with explicit local dynamics is studied. Unlike many patch-based metapopulation models which assume that the local population within each patch is at its equilibrium, our model incorporates population changes in local patches that interact with metapopulation dynamics. The model keeps track of the fractions of patches that have species 1 only, species 2 only, or both species. For patches with both species, the Lotka-Volterra type of competition is assumed. It is shown that when the local dynamics is coupled with the metapopulation dynamics the model outcomes can be very different comparing with metapopulation models that do not explicitly include local population dynamics. The analysis of the coupled system is carried out by using techniques in singular perturbation theory.
Citation: Dashun Xu, Z. Feng. A metapopulation model with local competitions. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 495-510. doi: 10.3934/dcdsb.2009.12.495
[1]

Zhilan Feng, Robert Swihart, Yingfei Yi, Huaiping Zhu. Coexistence in a metapopulation model with explicit local dynamics. Mathematical Biosciences & Engineering, 2004, 1 (1) : 131-145. doi: 10.3934/mbe.2004.1.131

[2]

Dianmo Li, Zengxiang Gao, Zufei Ma, Baoyu Xie, Zhengjun Wang. Two general models for the simulation of insect population dynamics. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 623-628. doi: 10.3934/dcdsb.2004.4.623

[3]

B. E. Ainseba, W. E. Fitzgibbon, M. Langlais, J. J. Morgan. An application of homogenization techniques to population dynamics models. Communications on Pure & Applied Analysis, 2002, 1 (1) : 19-33. doi: 10.3934/cpaa.2002.1.19

[4]

Robert Carlson. Myopic models of population dynamics on infinite networks. Networks & Heterogeneous Media, 2014, 9 (3) : 477-499. doi: 10.3934/nhm.2014.9.477

[5]

Nahla Abdellatif, Radhouane Fekih-Salem, Tewfik Sari. Competition for a single resource and coexistence of several species in the chemostat. Mathematical Biosciences & Engineering, 2016, 13 (4) : 631-652. doi: 10.3934/mbe.2016012

[6]

Cecilia Cavaterra, M. Grasselli. Robust exponential attractors for population dynamics models with infinite time delay. Discrete & Continuous Dynamical Systems - B, 2006, 6 (5) : 1051-1076. doi: 10.3934/dcdsb.2006.6.1051

[7]

L. M. Abia, O. Angulo, J.C. López-Marcos. Size-structured population dynamics models and their numerical solutions. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 1203-1222. doi: 10.3934/dcdsb.2004.4.1203

[8]

Cecilia Cavaterra, Maurizio Grasselli. Asymptotic behavior of population dynamics models with nonlocal distributed delays. Discrete & Continuous Dynamical Systems - A, 2008, 22 (4) : 861-883. doi: 10.3934/dcds.2008.22.861

[9]

Rabah Labbas, Keddour Lemrabet, Stéphane Maingot, Alexandre Thorel. Generalized linear models for population dynamics in two juxtaposed habitats. Discrete & Continuous Dynamical Systems - A, 2019, 39 (5) : 2933-2960. doi: 10.3934/dcds.2019122

[10]

Donald L. DeAngelis, Bo Zhang. Effects of dispersal in a non-uniform environment on population dynamics and competition: A patch model approach. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3087-3104. doi: 10.3934/dcdsb.2014.19.3087

[11]

Xueli Bai, Fang Li. Global dynamics of competition models with nonsymmetric nonlocal dispersals when one diffusion rate is small. Discrete & Continuous Dynamical Systems - A, 2019, 0 (0) : 0-0. doi: 10.3934/dcds.2020035

[12]

Hua Nie, Sze-Bi Hsu, Jianhua Wu. Coexistence solutions of a competition model with two species in a water column. Discrete & Continuous Dynamical Systems - B, 2015, 20 (8) : 2691-2714. doi: 10.3934/dcdsb.2015.20.2691

[13]

Georg Hetzer, Tung Nguyen, Wenxian Shen. Coexistence and extinction in the Volterra-Lotka competition model with nonlocal dispersal. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1699-1722. doi: 10.3934/cpaa.2012.11.1699

[14]

Yuan Lou, Daniel Munther. Dynamics of a three species competition model. Discrete & Continuous Dynamical Systems - A, 2012, 32 (9) : 3099-3131. doi: 10.3934/dcds.2012.32.3099

[15]

Wei Feng, Michael T. Cowen, Xin Lu. Coexistence and asymptotic stability in stage-structured predator-prey models. Mathematical Biosciences & Engineering, 2014, 11 (4) : 823-839. doi: 10.3934/mbe.2014.11.823

[16]

Benlong Xu, Hongyan Jiang. Invasion and coexistence of competition-diffusion-advection system with heterogeneous vs homogeneous resources. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4255-4266. doi: 10.3934/dcdsb.2018136

[17]

Jeremias Epperlein, Stefan Siegmund, Petr Stehlík, Vladimír  Švígler. Coexistence equilibria of evolutionary games on graphs under deterministic imitation dynamics. Discrete & Continuous Dynamical Systems - B, 2016, 21 (3) : 803-813. doi: 10.3934/dcdsb.2016.21.803

[18]

Wei Feng, Xin Lu, Richard John Donovan Jr.. Population dynamics in a model for territory acquisition. Conference Publications, 2001, 2001 (Special) : 156-165. doi: 10.3934/proc.2001.2001.156

[19]

Bingtuan Li. Some remarks on traveling wave solutions in competition models. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 389-399. doi: 10.3934/dcdsb.2009.12.389

[20]

Lih-Ing W. Roeger. Discrete May-Leonard competition models II. Discrete & Continuous Dynamical Systems - B, 2005, 5 (3) : 841-860. doi: 10.3934/dcdsb.2005.5.841

2018 Impact Factor: 1.008

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]