Source-only realizations, weakly reversible deficiency one networks and dynamical equivalence

2022/05/02 by Abhishek Deshpande, Deshpande, Abhishek
Neuroscience · Physics and Astronomy · #37N25 #80A30 #92C42 #92C45 #92D25 #Complex Network Analysis Techniques #Dynamical Systems (math.DS) #FOS: Mathematics #Neural dynamics and brain function #Opinion Dynamics and Social Influence

paper · pdf · doi:10.48550/arxiv.2205.00801

openalex publication_date 2022/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Reaction networks can display a wide array of dynamics. However, it is possible for different reaction networks to display the same dynamics. This phenomenon is called dynamical equivalence and makes network identification a hard problem to solve. We show that to find a strongly endotactic, endotactic, consistent, or conservative realization that is dynamically equivalent to the mass-action system generated by a given network, it suffices to consider only the source vertices of the given network. In addition, we show that weakly reversible deficiency one realizations are not unique. We also present a characterization of the dynamical relationships that exist between several types of weakly reversible deficiency one networks.

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