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arXiv · 2607.14143

The Planar Case of Thomas Positive Circuits Conjecture

Natan Katz
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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.

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Natan Katz. 2026-07-13. The Planar Case of Thomas Positive Circuits Conjecture. https://arxiv.org/abs/2607.14143

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