Carrying simplices in discrete competitive systems and age-structured semelparous populations

Previous Article
Impulsive control of Lagrangian systems and locomotion in fluids
DCDS Home
This Issue
Next Article
Weak-convergence methods for Hamiltonian multiscale problems

January 2008, 20(1): 37-52. doi: 10.3934/dcds.2008.20.37

Carrying simplices in discrete competitive systems and age-structured semelparous populations

Odo Diekmann ^1, , Yi Wang ^2, and Ping Yan ^3,

1.	Department of Mathematics, University of Utrecht, P.O. Box 80010, 3580 TA Utrecht, Netherlands
2.	Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, China
3.	Department of Mathematics and Statistics, University of Helsinki, FIN-00014 Helsinki, Finland

Received November 2006 Revised April 2007 Published October 2007

Abstract
Related Papers

For discrete competitive dynamical systems, amenable general conditions are presented to guarantee the existence of the carrying simplex and then these results are applied to age-structured semelparous population models, as well as to an annual plant competition model.

Keywords: Semelparous populations, Carrying simplex, Discrete competitive systems..

Mathematics Subject Classification: Primary: 92D25,39A10; Secondary: 37N2.

Citation: Odo Diekmann, Yi Wang, Ping Yan. Carrying simplices in discrete competitive systems and age-structured semelparous populations. Discrete & Continuous Dynamical Systems - A, 2008, 20 (1) : 37-52. doi: 10.3934/dcds.2008.20.37

[1]	Mats Gyllenberg, Jifa Jiang, Lei Niu, Ping Yan. On the classification of generalized competitive Atkinson-Allen models via the dynamics on the boundary of the carrying simplex. Discrete & Continuous Dynamical Systems - A, 2018, 38 (2) : 615-650. doi: 10.3934/dcds.2018027
[2]	Kokum R. De Silva, Tuoc V. Phan, Suzanne Lenhart. Advection control in parabolic PDE systems for competitive populations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 1049-1072. doi: 10.3934/dcdsb.2017052
[3]	M. R. S. Kulenović, Orlando Merino. Global bifurcation for discrete competitive systems in the plane. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 133-149. doi: 10.3934/dcdsb.2009.12.133
[4]	Stephen Baigent. Convex geometry of the carrying simplex for the May-Leonard map. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1697-1723. doi: 10.3934/dcdsb.2018288
[5]	P. Adda, J. L. Dimi, A. Iggidir, J. C. Kamgang, G. Sallet, J. J. Tewa. General models of host-parasite systems. Global analysis. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 1-17. doi: 10.3934/dcdsb.2007.8.1
[6]	Thuc Manh Le, Nguyen Van Minh. Monotone traveling waves in a general discrete model for populations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (8) : 3221-3234. doi: 10.3934/dcdsb.2017171
[7]	Denis de Carvalho Braga, Luis Fernando Mello, Carmen Rocşoreanu, Mihaela Sterpu. Lyapunov coefficients for non-symmetrically coupled identical dynamical systems. Application to coupled advertising models. Discrete & Continuous Dynamical Systems - B, 2009, 11 (3) : 785-803. doi: 10.3934/dcdsb.2009.11.785
[8]	Susanna Terracini, Juncheng Wei. DCDS-A Special Volume Qualitative properties of solutions of nonlinear elliptic equations and systems. Preface. Discrete & Continuous Dynamical Systems - A, 2014, 34 (6) : i-ii. doi: 10.3934/dcds.2014.34.6i
[9]	Anna Kostianko, Sergey Zelik. Inertial manifolds for 1D reaction-diffusion-advection systems. Part Ⅰ: Dirichlet and Neumann boundary conditions. Communications on Pure & Applied Analysis, 2017, 16 (6) : 2357-2376. doi: 10.3934/cpaa.2017116
[10]	Anna Kostianko, Sergey Zelik. Inertial manifolds for 1D reaction-diffusion-advection systems. Part Ⅱ: periodic boundary conditions. Communications on Pure & Applied Analysis, 2018, 17 (1) : 285-317. doi: 10.3934/cpaa.2018017
[11]	M. R. S. Kulenović, Orlando Merino. Competitive-exclusion versus competitive-coexistence for systems in the plane. Discrete & Continuous Dynamical Systems - B, 2006, 6 (5) : 1141-1156. doi: 10.3934/dcdsb.2006.6.1141
[12]	James Sandefur. A unifying approach to discrete single-species populations models. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 493-508. doi: 10.3934/dcdsb.2017194
[13]	Eduardo Liz. A new flexible discrete-time model for stable populations. Discrete & Continuous Dynamical Systems - B, 2018, 23 (6) : 2487-2498. doi: 10.3934/dcdsb.2018066
[14]	H. L. Smith, X. Q. Zhao. Competitive exclusion in a discrete-time, size-structured chemostat model. Discrete & Continuous Dynamical Systems - B, 2001, 1 (2) : 183-191. doi: 10.3934/dcdsb.2001.1.183
[15]	David M. Chan, Matt McCombs, Sarah Boegner, Hye Jin Ban, Suzanne L. Robertson. Extinction in discrete, competitive, multi-species patch models. Discrete & Continuous Dynamical Systems - B, 2015, 20 (6) : 1583-1590. doi: 10.3934/dcdsb.2015.20.1583
[16]	Ryusuke Kon. Dynamics of competitive systems with a single common limiting factor. Mathematical Biosciences & Engineering, 2015, 12 (1) : 71-81. doi: 10.3934/mbe.2015.12.71
[17]	Zhanyuan Hou, Stephen Baigent. Heteroclinic limit cycles in competitive Kolmogorov systems. Discrete & Continuous Dynamical Systems - A, 2013, 33 (9) : 4071-4093. doi: 10.3934/dcds.2013.33.4071
[18]	J. M. Cushing. Nonlinear semelparous Leslie models. Mathematical Biosciences & Engineering, 2006, 3 (1) : 17-36. doi: 10.3934/mbe.2006.3.17
[19]	Mădălina Roxana Buneci. Morphisms of discrete dynamical systems. Discrete & Continuous Dynamical Systems - A, 2011, 29 (1) : 91-107. doi: 10.3934/dcds.2011.29.91
[20]	Mats Gyllenberg, Yi Wang. Periodic tridiagonal systems modeling competitive-cooperative ecological interactions. Discrete & Continuous Dynamical Systems - B, 2005, 5 (2) : 289-298. doi: 10.3934/dcdsb.2005.5.289

2018 Impact Factor: 1.143

American Institute of Mathematical Sciences