Abstract
In this paper, we merge two theories: that of pulse processes on weighted digraphs and that of evolution algebras. We enrich both of them. In fact, we obtain new results in the theory of pulse processes thanks to the new algebraic tool that we introduce in its framework, also extending the theory of evolution algebras, as well as its applications.
Highlights
A complex system can be understood as a system determined by many components which may interact with each other
We established the connection between the theory of pulse processes and the theory of evolution algebras
Since we are simultaneously dealing with two theories, the motivation increases as it comes from two different sources. This would be the case of Proposition 1 and Corollary 4
Summary
A complex system can be understood as a system determined by many components which may interact with each other (see [1] for a deeper discussion about the term). In the last report [20], pulse processes were used in the context of energy demand, air pollution, and related environmental problems in order to analyze the transportation system of a hypothetical metropolitan area similar to San Diego, California As it is stated in R-756-NSF, the result of using graph theory to model such problems, “while it does not necessarily provide a complete solution to the problem, it often brings a better understanding of what the possible solutions are or an insight into the qualitative interrelationships that underlie the problem, or an identification of significant or vulnerable points of attack”. With the examples quoted above, we show in an explicit way how the reduction process simplifies and enriches the analysis achieved in [20]
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