Lotka–Volterra coalgebras

Arenas, Manuel; Labra, Antonieta; Paniello, Irene

doi:10.1080/03081087.2021.1882372

Cited by 7 publications

(3 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An evolution algebra E is called an S-evolution algebra if its structural matrix is an S-matrix. If a structural matrix is skew-symmetric, then the corresponding evolution algebra is called Lotka-Volterra (or Volterra) evolution algebra [34,40]. One can see that any Lotka-Volterra algebras form a class of S-evolution algebras.…”

Section: S-evolution Algebrasmentioning

confidence: 99%

On Extendibility of Evolution Subalgebras Generated by Idempotents

Mukhamedov

Qaralleh

2023

Mathematics

View full text Add to dashboard Cite

In the present paper, we examined the extendibility of evolution subalgebras generated by idempotents of evolution algebras. The extendibility of the isomorphism of such subalgebras to the entire algebra was investigated. Moreover, the existence of an evolution algebra generated by arbitrary idempotents was also studied. Furthermore, we described the tensor product of algebras generated by arbitrary idempotents and found the conditions of the tensor decomposability of four-dimensional S-evolution algebras. This paper’s findings shed light on the field of algebraic structures, particularly in studying evolution algebras. By examining the extendibility of evolution subalgebras generated by idempotents, we provide insights into the structural properties and relationships within these algebras. Understanding the isomorphism of such subalgebras and their extension allows a deeper comprehension of the overall algebraic structure and its behaviour.

show abstract

Section: S-evolution Algebrasmentioning

confidence: 99%

On Extendibility of Evolution Subalgebras Generated by Idempotents

Mukhamedov

Qaralleh

2023

Mathematics

View full text Add to dashboard Cite

show abstract

“…We note that evolution algebras corresponding to skew-symmetric matrices are called Lotka-Volterra (or Volterra) evolution algebras. Such kind of algebras have been investigated in [30,39]. From the given Example 1, we can see that Lotka-Volterra algebras and S-evolution algebras (different from those ones) may not share common properties.…”

Section: S-evolution Algebras and Their Graphsmentioning

confidence: 99%

On S-Evolution Algebras and Their Enveloping Algebras

Mukhamedov

Qaralleh

2021

Mathematics

View full text Add to dashboard Cite

In the present paper, we introduce S-evolution algebras and investigate their solvability, simplicity, and semisimplicity. The structure of enveloping algebras has been carried out through the attached graph of S-evolution algebras. Moreover, we introduce the concept of E-linear derivation of S-evolution algebras, and prove such derivations can be extended to their enveloping algebras under certain conditions.

show abstract

“…Recently, in [ 38 , 39 , 40 , 41 ], derivations of Lotka–Volterra algebras have been described. Furthermore, other types of genetic algebras have been investigated in [ 42 , 43 , 44 , 45 , 46 , 47 ].…”

Section: Introductionmentioning

confidence: 99%

Genetic Algebras Associated with ξ(a)-Quadratic Stochastic Operators

Mukhamedov,

Qaralleh,

Qaisar

et al. 2023

Entropy

View full text Add to dashboard Cite

The present paper deals with a class of ξ(a)-quadratic stochastic operators, referred to as QSOs, on a two-dimensional simplex. It investigates the algebraic properties of the genetic algebras associated with ξ(a)-QSOs. Namely, the associativity, characters and derivations of genetic algebras are studied. Moreover, the dynamics of these operators are also explored. Specifically, we focus on a particular partition that results in nine classes, which are further reduced to three nonconjugate classes. Each class gives rise to a genetic algebra denoted as Ai, and it is shown that these algebras are isomorphic. The investigation then delves into analyzing various algebraic properties within these genetic algebras, such as associativity, characters, and derivations. The conditions for associativity and character behavior are provided. Furthermore, a comprehensive analysis of the dynamic behavior of these operators is conducted.

show abstract

Lotka–Volterra coalgebras

Cited by 7 publications

References 9 publications

On Extendibility of Evolution Subalgebras Generated by Idempotents

On Extendibility of Evolution Subalgebras Generated by Idempotents

On S-Evolution Algebras and Their Enveloping Algebras

Genetic Algebras Associated with ξ(a)-Quadratic Stochastic Operators

Contact Info

Product

Resources

About