ABSTRACT

We consider an evolution algebra identifying the coefficients of SIS–SIR worm propagation models as the structure constants of the algebra. The basic properties of this algebra are studied. We prove that it is a commutative (and hence flexible), not associative and baric algebra. We describe the full set of idempotent elements and the full set of absolute nilpotent elements. We find all the fixed points of the dynamical systems. We also study several properties of the algebra connecting them to dynamical systems.

中文翻译：

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蠕虫传播模型的演化代数和动力学系统

摘要

我们考虑一个进化代数，该代数将SIS–SIR蠕虫传播模型的系数标识为代数的结构常数。研究了该代数的基本性质。我们证明它是一个可交换的（因而是灵活的），而不是关联代数和重代数。我们描述了幂等元素的完整集合和绝对幂等元素的完整集合。我们找到了动力学系统的所有固定点。我们还研究了代数的一些性质，将它们连接到动力学系统。