Polynomial Dynamical Systems, Reaction Networks, and Toric Differential Inclusions

DOI10.1137/17M1129076zbMath1412.37035arXiv1901.02544OpenAlexW2911202212WikidataQ115246941 ScholiaQ115246941MaRDI QIDQ5742690

Gheorghe Craciun

Publication date: 8 May 2019

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.02544

zbMATH Keywords

persistenceglobal attractor conjecturepolynomial dynamical systemsreaction networkstoric differential inclusions

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Dynamical systems in biology (37N25) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08) Dynamical aspects of statistical mechanics (37A60) Nonautonomous smooth dynamical systems (37C60)

Related Items (22)

Disguised toric dynamical systems ⋮ Multistationarity in cyclic sequestration-transmutation networks ⋮ Absolute concentration robustness in networks with low-dimensional stoichiometric subspace ⋮ A new decomposition of the graph Laplacian and the binomial structure of mass-action systems ⋮ On the stability of discrete-time homogeneous polynomial dynamical systems ⋮ The Disguised Toric Locus and Affine Equivalence of Reaction Networks ⋮ Source-Only Realizations, Weakly Reversible Deficiency One Networks, and Dynamical Equivalence ⋮ On the connectivity of the disguised toric locus of a reaction network ⋮ Polyhedral geometry and combinatorics of an autocatalytic ecosystem ⋮ On classes of reaction networks and their associated polynomial dynamical systems ⋮ Robust Persistence and Permanence of Polynomial and Power Law Dynamical Systems ⋮ Quasi-toric differential inclusions ⋮ Finite-time stability of impulsive differential inclusion: applications to discontinuous impulsive neural networks ⋮ A generalization of Birch's theorem and vertex-balanced steady states for generalized mass-action systems ⋮ Endotactic Networks and Toric Differential Inclusions ⋮ A reaction network approach to the convergence to equilibrium of quantum Boltzmann equations for Bose gases ⋮ Uniqueness of weakly reversible and deficiency zero realizations of dynamical systems ⋮ Single-target networks ⋮ Minimal invariant regions and minimal globally attracting regions for toric differential inclusions ⋮ Minimal invariant regions and minimal globally attracting regions for variable-k reaction systems ⋮ Homeostasis and injectivity: a reaction network perspective ⋮ Autocatalytic recombination systems: a reaction network perspective

Cites Work

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