Conservative and dissipative polymatrix replicators

Alishah, Hassan Najafi; Duarte, Pedro; Peixe, Telmo

doi:10.3934/jdg.2015.2.157

Cited by 5 publications

(16 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then the vector field X is permanent. (2') for any ω-limit orbit x(t) in ∂Γ n , T 0 Ψ(x(t)) dt > 0 for some T > 0, we have that condition (2') implies (2).…”

mentioning

confidence: 88%

“…where d is the Euclidean distance, ϕ t denotes the flow determined by system (2) and ∂∆ n−1 is the boundary of ∆ n−1 .…”

Section: Theorem 22 If the Replicator Equationmentioning

confidence: 99%

“…Theorem 2.4. Let X be the replicator vector field defined by (2). If there is a point p ∈ int(∆ n−1 ) such that for all boundary equilibria x ∈ ∂∆ n−1 ,…”

Section: Theorem 22 If the Replicator Equationmentioning

confidence: 99%

“…Alishah and P. Duarte [1] introduced the model that they designated as polymatrix games to study this kind of population. In [2] H. Alishah, P. Duarte and T. Peixe study particular classes of polymatrix games. The system of ordinary differential equations, designated as the polymatrix replicator, that model this game, will be presented in detail in section 3.…”

mentioning

confidence: 99%

“…In this section we present the definition of the polymatrix replicator. For more details on the subject, namely some of its properties or special classes, see [1] and [2].…”

mentioning

confidence: 99%

See 4 more Smart Citations

Permanence in polymatrix replicators

Peixe¹,

Mathematics²

2021

Journal of Dynamics &Amp; Games

Self Cite

View full text Add to dashboard Cite

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 [15] introduced the concept of permanence as a stability notion for systems that models the self-organization of biological macromolecules. After, in 1987 W. Jansen [9], and J. Hofbauer and K. Sigmund [6] give sufficient conditions for permanence in the replicator equations. In this paper we extend these results for polymatrix replicators.

show abstract

“…Then the vector field X is permanent. (2') for any ω-limit orbit x(t) in ∂Γ n , T 0 Ψ(x(t)) dt > 0 for some T > 0, we have that condition (2') implies (2).…”

mentioning

confidence: 88%

“…where d is the Euclidean distance, ϕ t denotes the flow determined by system (2) and ∂∆ n−1 is the boundary of ∆ n−1 .…”

Section: Theorem 22 If the Replicator Equationmentioning

confidence: 99%

“…Theorem 2.4. Let X be the replicator vector field defined by (2). If there is a point p ∈ int(∆ n−1 ) such that for all boundary equilibria x ∈ ∂∆ n−1 ,…”

Section: Theorem 22 If the Replicator Equationmentioning

confidence: 99%

mentioning

confidence: 99%

“…In this section we present the definition of the polymatrix replicator. For more details on the subject, namely some of its properties or special classes, see [1] and [2].…”

mentioning

confidence: 99%

See 3 more Smart Citations