The Planar Case of Thomas Positive Circuits Conjecture
arXiv:2607.14143
summary
The paper investigates conditions under which Thomas' positive circuits conjecture holds for planar dynamical systems, using tools from dynamical systems theory and planar analysis.
Abstract
The notion of circuit refers to a cyclic oriented influence between the elements of a dynamical system. There are two classes of circuit: positive and negative. R. Thomas conjectured that a necessary condition of multi stationarity is the existence of positive circuits. In this paper we use dynamical system tools and planar analysis to find conditions for which the conjecture holds for planar systems.
Topics & keywords
#positive circuits#thomas conjecture#planar systems#multistationarity#cyclic influencepositive circuitThomas conjectureplanar dynamical systemmultistationarityoriented influence