
-
Previous Article
A Mean Field Games model for finite mixtures of Bernoulli and categorical distributions
- JDG Home
- This Issue
-
Next Article
Generalized intransitive dice: Mimicking an arbitrary tournament
Permanence in polymatrix replicators
ISEG-Lisbon School of Economics & Management, Universidade de Lisboa, REM-Research in Economics and Mathematics, CEMAPRE-Centro de Matemática Aplicada à Previsão e Decisão Económica |
Generally a biological system is said to be permanent if under small perturbations none of the species goes to extinction. In 1979 P. Schuster, K. Sigmund, and R. Wolff [
References:
[1] |
H. N. Alishah and P. Duarte,
Hamiltonian evolutionary games, Journal of Dynamics and Games, 2 (2015), 33-49.
doi: 10.3934/jdg.2015.2.33. |
[2] |
H. N. Alishah, P. Duarte and T. Peixe,
Conservative and dissipative polymatrix replicators, Journal of Dynamics and Games, 2 (2015), 157-185.
doi: 10.3934/jdg.2015.2.157. |
[3] |
H. N. Alishah, P. Duarte and T. Peixe,
Asymptotic Poincaré maps along the edges of polytopes, Nonlinearity, 33 (2020), 469-510.
doi: 10.1088/1361-6544/ab49e6. |
[4] |
P. Duarte, R. L. Fernandes and W. M. Oliva,
Dynamics of the attractor in the Lotka-Volterra equations, J. Differential Equations, 149 (1998), 143-189.
doi: 10.1006/jdeq.1998.3443. |
[5] |
J. Hofbauer,
On the occurrence of limit cycles in the Volterra-Lotka equation, Nonlinear Anal., 5 (1981), 1003-1007.
doi: 10.1016/0362-546X(81)90059-6. |
[6] |
J. Hofbauer and K. Sigmund, Permanence for Replicator Equations, Springer Berlin Heidelberg, 1987.
doi: 10.1007/978-3-662-00748-8_7. |
[7] |
J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge University Press, Cambridge, 1998.
doi: 10.1017/CBO9781139173179.![]() ![]() |
[8] |
J. Hofbauer,
A general cooperation theorem for hypercycles, Monatsh. Math., 91 (1981), 233-240.
doi: 10.1007/BF01301790. |
[9] |
W. Jansen,
A permanence theorem for replicator and Lotka-Volterra systems, J. Math. Biol., 25 (1987), 411-422.
doi: 10.1007/BF00277165. |
[10] |
A. J. Lotka, Elements of mathematical biology. (formerly published under the title Elements of Physical Biology), Dover Publications, Inc., New York, 1958.
doi: 10.1002/jps.3030471044. |
[11] |
J. M. Smith,
The logic of animal conflict, Nature, 246 (1973), 15-18.
doi: 10.1038/246015a0. |
[12] |
P. Schuster and K. Sigmund,
Coyness, philandering and stable strategies, Animal Behaviour, 29 (1981), 186-192.
doi: 10.1016/S0003-3472(81)80165-0. |
[13] |
P. Schuster and K. Sigmund,
Replicator dynamics, J. Theoret. Biol., 100 (1983), 533-538.
doi: 10.1016/0022-5193(83)90445-9. |
[14] |
P. Schuster, K. Sigmund, J. Hofbauer and R. Wolff,
Self-regulation of behaviour in animal societies, Biol. Cybernet., 40 (1981), 9-15.
doi: 10.1007/BF00326676. |
[15] |
P. Schuster, K. Sigmund and R. Wolff,
Dynamical systems under constant organization. ⅲ. cooperative and competitive behavior of hypercycles, Journal of Differential Equations, 32 (1979), 357-368.
doi: 10.1016/0022-0396(79)90039-1. |
[16] |
P. D. Taylor and L. B. Jonker,
Evolutionarily stable strategies and game dynamics, Math. Biosci., 40 (1978), 145-156.
doi: 10.1016/0025-5564(78)90077-9. |
[17] |
V. Volterra, Leç cons sur la Théorie Mathématique de la Lutte pour la Vie (Reprint of the 1931 original), Éditions Jacques Gabay, Sceaux, 1990. |
[18] |
J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, New Jersey, 1944.
![]() |
show all references
References:
[1] |
H. N. Alishah and P. Duarte,
Hamiltonian evolutionary games, Journal of Dynamics and Games, 2 (2015), 33-49.
doi: 10.3934/jdg.2015.2.33. |
[2] |
H. N. Alishah, P. Duarte and T. Peixe,
Conservative and dissipative polymatrix replicators, Journal of Dynamics and Games, 2 (2015), 157-185.
doi: 10.3934/jdg.2015.2.157. |
[3] |
H. N. Alishah, P. Duarte and T. Peixe,
Asymptotic Poincaré maps along the edges of polytopes, Nonlinearity, 33 (2020), 469-510.
doi: 10.1088/1361-6544/ab49e6. |
[4] |
P. Duarte, R. L. Fernandes and W. M. Oliva,
Dynamics of the attractor in the Lotka-Volterra equations, J. Differential Equations, 149 (1998), 143-189.
doi: 10.1006/jdeq.1998.3443. |
[5] |
J. Hofbauer,
On the occurrence of limit cycles in the Volterra-Lotka equation, Nonlinear Anal., 5 (1981), 1003-1007.
doi: 10.1016/0362-546X(81)90059-6. |
[6] |
J. Hofbauer and K. Sigmund, Permanence for Replicator Equations, Springer Berlin Heidelberg, 1987.
doi: 10.1007/978-3-662-00748-8_7. |
[7] |
J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge University Press, Cambridge, 1998.
doi: 10.1017/CBO9781139173179.![]() ![]() |
[8] |
J. Hofbauer,
A general cooperation theorem for hypercycles, Monatsh. Math., 91 (1981), 233-240.
doi: 10.1007/BF01301790. |
[9] |
W. Jansen,
A permanence theorem for replicator and Lotka-Volterra systems, J. Math. Biol., 25 (1987), 411-422.
doi: 10.1007/BF00277165. |
[10] |
A. J. Lotka, Elements of mathematical biology. (formerly published under the title Elements of Physical Biology), Dover Publications, Inc., New York, 1958.
doi: 10.1002/jps.3030471044. |
[11] |
J. M. Smith,
The logic of animal conflict, Nature, 246 (1973), 15-18.
doi: 10.1038/246015a0. |
[12] |
P. Schuster and K. Sigmund,
Coyness, philandering and stable strategies, Animal Behaviour, 29 (1981), 186-192.
doi: 10.1016/S0003-3472(81)80165-0. |
[13] |
P. Schuster and K. Sigmund,
Replicator dynamics, J. Theoret. Biol., 100 (1983), 533-538.
doi: 10.1016/0022-5193(83)90445-9. |
[14] |
P. Schuster, K. Sigmund, J. Hofbauer and R. Wolff,
Self-regulation of behaviour in animal societies, Biol. Cybernet., 40 (1981), 9-15.
doi: 10.1007/BF00326676. |
[15] |
P. Schuster, K. Sigmund and R. Wolff,
Dynamical systems under constant organization. ⅲ. cooperative and competitive behavior of hypercycles, Journal of Differential Equations, 32 (1979), 357-368.
doi: 10.1016/0022-0396(79)90039-1. |
[16] |
P. D. Taylor and L. B. Jonker,
Evolutionarily stable strategies and game dynamics, Math. Biosci., 40 (1978), 145-156.
doi: 10.1016/0025-5564(78)90077-9. |
[17] |
V. Volterra, Leç cons sur la Théorie Mathématique de la Lutte pour la Vie (Reprint of the 1931 original), Éditions Jacques Gabay, Sceaux, 1990. |
[18] |
J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, New Jersey, 1944.
![]() |

Vertices of |
|
|
|
Vertices of |
|
|
|
Equilibria on |
|
|
|
Equilibria on |
|
|
|
Equilibria on |
|
|
|
Equilibria on |
|
|
|
Equilibria on |
|
|
|
Equilibria on |
|
|
|
[1] |
Guo-Bao Zhang, Ruyun Ma, Xue-Shi Li. Traveling waves of a Lotka-Volterra strong competition system with nonlocal dispersal. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 587-608. doi: 10.3934/dcdsb.2018035 |
[2] |
Dan Wei, Shangjiang Guo. Qualitative analysis of a Lotka-Volterra competition-diffusion-advection system. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2599-2623. doi: 10.3934/dcdsb.2020197 |
[3] |
David Cantala, Juan Sebastián Pereyra. Endogenous budget constraints in the assignment game. Journal of Dynamics & Games, 2015, 2 (3&4) : 207-225. doi: 10.3934/jdg.2015002 |
[4] |
Tao Wu, Yu Lei, Jiao Shi, Maoguo Gong. An evolutionary multiobjective method for low-rank and sparse matrix decomposition. Big Data & Information Analytics, 2017, 2 (1) : 23-37. doi: 10.3934/bdia.2017006 |
[5] |
Shangzhi Li, Shangjiang Guo. Permanence and extinction of a stochastic SIS epidemic model with three independent Brownian motions. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2693-2719. doi: 10.3934/dcdsb.2020201 |
[6] |
Guillaume Bal, Wenjia Jing. Homogenization and corrector theory for linear transport in random media. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1311-1343. doi: 10.3934/dcds.2010.28.1311 |
[7] |
Felix Finster, Jürg Fröhlich, Marco Oppio, Claudio F. Paganini. Causal fermion systems and the ETH approach to quantum theory. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1717-1746. doi: 10.3934/dcdss.2020451 |
[8] |
W. Cary Huffman. On the theory of $\mathbb{F}_q$-linear $\mathbb{F}_{q^t}$-codes. Advances in Mathematics of Communications, 2013, 7 (3) : 349-378. doi: 10.3934/amc.2013.7.349 |
[9] |
John Leventides, Costas Poulios, Georgios Alkis Tsiatsios, Maria Livada, Stavros Tsipras, Konstantinos Lefcaditis, Panagiota Sargenti, Aleka Sargenti. Systems theory and analysis of the implementation of non pharmaceutical policies for the mitigation of the COVID-19 pandemic. Journal of Dynamics & Games, 2021 doi: 10.3934/jdg.2021004 |
[10] |
Vladimir Georgiev, Sandra Lucente. Focusing nlkg equation with singular potential. Communications on Pure & Applied Analysis, 2018, 17 (4) : 1387-1406. doi: 10.3934/cpaa.2018068 |
[11] |
Daoyin He, Ingo Witt, Huicheng Yin. On the strauss index of semilinear tricomi equation. Communications on Pure & Applied Analysis, 2020, 19 (10) : 4817-4838. doi: 10.3934/cpaa.2020213 |
[12] |
Diana Keller. Optimal control of a linear stochastic Schrödinger equation. Conference Publications, 2013, 2013 (special) : 437-446. doi: 10.3934/proc.2013.2013.437 |
[13] |
Simone Cacace, Maurizio Falcone. A dynamic domain decomposition for the eikonal-diffusion equation. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 109-123. doi: 10.3934/dcdss.2016.9.109 |
[14] |
Naeem M. H. Alkoumi, Pedro J. Torres. Estimates on the number of limit cycles of a generalized Abel equation. Discrete & Continuous Dynamical Systems - A, 2011, 31 (1) : 25-34. doi: 10.3934/dcds.2011.31.25 |
[15] |
Jumpei Inoue, Kousuke Kuto. On the unboundedness of the ratio of species and resources for the diffusive logistic equation. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2441-2450. doi: 10.3934/dcdsb.2020186 |
[16] |
Wentao Huang, Jianlin Xiang. Soliton solutions for a quasilinear Schrödinger equation with critical exponent. Communications on Pure & Applied Analysis, 2016, 15 (4) : 1309-1333. doi: 10.3934/cpaa.2016.15.1309 |
[17] |
Kin Ming Hui, Soojung Kim. Asymptotic large time behavior of singular solutions of the fast diffusion equation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (11) : 5943-5977. doi: 10.3934/dcds.2017258 |
[18] |
Thierry Cazenave, Ivan Naumkin. Local smooth solutions of the nonlinear Klein-gordon equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1649-1672. doi: 10.3934/dcdss.2020448 |
[19] |
Jiaquan Liu, Xiangqing Liu, Zhi-Qiang Wang. Sign-changing solutions for a parameter-dependent quasilinear equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1779-1799. doi: 10.3934/dcdss.2020454 |
[20] |
Murat Uzunca, Ayşe Sarıaydın-Filibelioǧlu. Adaptive discontinuous galerkin finite elements for advective Allen-Cahn equation. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 269-281. doi: 10.3934/naco.2020025 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]