Evolution Algebras and their Applications

Tian, Jianjun Paul

doi:10.1007/978-3-540-74284-5

Cited by 136 publications

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“…In this paper, we employ the SpecExplorer 2 and the Graphwalker 3 generation engine that do not operate directly on UML, but on closely related concepts. The SpecExplorer input is actually based on a textual representation of an Abstract State Machine (ASM) [7] which is called Spec#. On contrast, the input for Graphwalker is GraphML, a XML format for describing graph structures.…”

Section: Problem Statementmentioning

confidence: 99%

Abstractions on Test Design Techniques

Wendland

2014

Annals of Computer Science and Information Systems

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Section: Problem Statementmentioning

confidence: 99%

Abstractions on Test Design Techniques

Wendland

2014

Annals of Computer Science and Information Systems

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“…In [15] an evolution algebra (EA) was introduced, (denoted by E) which is an algebra over a field with a basis on which multiplication is defined by the product of distinct basis terms being zero. This EA is commutative, but not necessarily associative or powerassociative [15].…”

Section: Introductionmentioning

confidence: 99%

“…This EA is commutative, but not necessarily associative or powerassociative [15]. Under some conditions on the matrix of structural constants the algebra E is a baric algebra [2].…”

Section: Introductionmentioning

confidence: 99%

“…This algebra is a natural generalization of the algebra A of free population. Moreover, the evolution algebra of a bisexual population B is different from the EA E defined in [15]. In fact, the table of multiplications of E non-zero multiplications are only the square of each basis element.…”

Section: Introductionmentioning

confidence: 99%

“…The properties of the algebras can be studied by the dynamical systems generated by the operator V . Note that for E the operator V is a linear operator [15], for other mentioned above algebras the operator V is a quadratic operator [2], [5], [8], [10], [13], [14].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Constrained evolution algebras and dynamical systems of a bisexual population

Dzhumadil’daev

Omirov²,

Rozikov³

2016

Linear Algebra and its Applications

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Abstract. Consider a bisexual population such that the set of females can be partitioned into finitely many different types indexed by {1, 2, . . . , n} and, similarly, that the male types are indexed by {1, 2, . . . , ν}. Recently an evolution algebra of bisexual population was introduced by identifying the coefficients of inheritance of a bisexual population as the structure constants of the algebra. In this paper we study constrained evolution algebra of bisexual population in which type "1" of females and males have preference. For such algebras sets of idempotent and absolute nilpotent elements are known. We consider two particular cases of this algebra, giving more constrains on the structural constants of the algebra. By the first our constrain we obtain an n + ν-dimensional algebra with a matrix of structural constants containing only 0 and 1. In the second case we consider n = ν = 2 but with general constrains. In both cases we study dynamical systems generated by the quadratic evolution operators of corresponding constrained algebras. We find all fixed points, limit points and some 2-periodic points of the dynamical systems. Moreover we study several properties of the constrained algebras connecting them to the dynamical systems. We give some biological interpretation of our results.Mathematics Subject Classifications (2010). 17D99; 60J10.

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Evolution algebras whose evolution operator is a homomorphism

Fernández-Ternero

Gómez-Sousa

Valdés

2021

Comp and Math Methods

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This article deals with the evolution operator of evolution algebras. We give a theorem that allows to characterize these algebras when this operator is a homomorphism of algebras of rank n−2 and this result in turn allows us to extend the classification of this type of algebras, given in a previous result by ourselves in 2021, up to the case of dimension 4. For this purpose, we analyze and make use of an algorithm for the degenerate case. A computational study of the procedure is also made.

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Evolution Algebras and their Applications

Abstract: The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Cited by 136 publications

References 0 publications

Abstractions on Test Design Techniques

Abstractions on Test Design Techniques

Constrained evolution algebras and dynamical systems of a bisexual population

Evolution algebras whose evolution operator is a homomorphism

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