English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The connection between network topology and stability remains unclear.General approaches that clarify this relationship and allow for more efficientstability analysis would be desirable. Inspired by chemical reaction networks,I demonstrate the utility of expressing the governing equations of arbitraryfirst-order dynamical systems (interaction networks) in terms of sums of realfunctions (generalized reactions) multiplied by real scalars (generalizedstoichiometries). Specifically, I examine the mathematical notion of influencetopology, which is based on the reaction stoichiometries and the firstderivatives of the reactions with respect to each species at the steady statesolution(s). It is naturally represented as a signed directed bipartite graphwith arrows or blunt arrows connecting a species node to a reaction node(positive/negative derivative) or a reaction node to a species node(positive/negative stoichiometry). The set of all such graphs is denumerable. Asignificant reduction in dimensionality is possible through stoichiometricscaling, cycle compaction, and temporal scaling. All cycles in a network can beread directly from the graph of its influence topology, enabling efficient andintuitive computation of the principal minors (sums of products ofnon-overlapping bipartite cycles) and the Hurwitz determinants (sums ofproducts of either the principal minors or the bipartite cycles) for testingsteady state stability. The stability of a given network is shown to have ahierarchical dependence first on its influence topology and then, morespecifically, on algebraic conditions (exact functional form of the reactions).The utility of this hierarchical approach to bifurcation analysis isdemonstrated on classical networks from control theory, biology, chemistry,physics, and electronics.

Efficient hierarchical analysis of the stability of a network through dimensional reduction of its influence topology