Rank of stably dissipative graphs
Pedro Duarte,Telmo Peixe +1 more
TLDR
For the class of stably dissipative Lotka-Volterra systems, the rank of the defining matrix, which is the dimension of the associated invariant foliation, is completely determined by the system's graph.About:
This article is published in Linear Algebra and its Applications.The article was published on 2012-11-15 and is currently open access. It has received 6 citations till now. The article focuses on the topics: Dissipative system & Invariant (mathematics).read more
Citations
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Journal ArticleDOI
Conservative and Dissipative Polymatrix Replicators
TL;DR: In this paper, the authors address a class of replicator dynamics, referred as polymatrix replicators, that contains well known classes of evolutionary game dynamics, such as the symmetric and asymmetric replicator equations, and some replicators equations for $n$-person games.
Dissertation
Lotka-volterra systems and polymatrix replicators
TL;DR: Tese de doutoramento, Matematica (Analise Matematicsa), Universidade de Lisboa, Faculdade de Ciencias, 2015 as discussed by the authors
Journal ArticleDOI
A survey on stably dissipative Lotka-Volterra systems with an application to infinite dimensional Volterra equations
TL;DR: In this article, it was shown that for stably dissipative Lotka-Volterra equations, the dynamics on the attractor are Hamiltonian and complex dynamics can occur.
Journal ArticleDOI
Conservative and Dissipative Polymatrix Replicators
TL;DR: In this paper, the authors address a class of replicator dynamics, referred as polymatrix replicators, that contains well known classes of evolutionary game dynamics, such as the symmetric and asymmetric (or bimatrix) replicator equations, and some replicators equations for $n$-person games.
References
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Book
Evolutionary games and population dynamics
Josef Hofbauer,Karl Sigmund +1 more
TL;DR: In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behavior, and of the closely related interactions among species in ecological communities.
Journal ArticleDOI
Stability theory for ordinary differential equations.
TL;DR: LaSalle stability theorems refined for ordinary differential equations, discussing classical Liapunov results on system stability were discussed in this article, where they were refined for the case of continuous systems.
Book
Global Dynamical Properties of Lotka-Volterra Systems
TL;DR: Reading global dynamical properties of lotka volterra systems is also a way as one of the collective books that gives many advantages.
Journal ArticleDOI
Systems of Differential Equations Which Are Competitive or Cooperative: I. Limit Sets
TL;DR: In this article, it was shown that limit sets of such systems cannot be more complicated than invariant sets of systems of one lower dimension, and orthogonal projection along any positive direction maps a limit set homeomorphically and equivariantly onto an invariant set of a Lipschitz vector field in a hyperplane.
Related Papers (5)
Classification and dynamics of stably dissipative Lotka–Volterra systems
Xiaohua Zhao,Jigui Luo +1 more
On a Hamiltonian version of a three-dimensional Lotka–Volterra system
Răzvan M. Tudoran,Anania Gîrban +1 more