Corpus ID: 219179381

Disguised toric dynamical systems

  title={Disguised toric dynamical systems},
  author={Laura Brustenga i Moncus'i and Gheorghe Craciun and Miruna-Stefana Sorea},
  journal={arXiv: Algebraic Geometry},
We study families of polynomial dynamical systems inspired by biochemical reaction networks. We focus on complex balanced mass-action systems, which have also been called toric dynamical systems. These systems are known or conjectured to enjoy very strong dynamical properties, such as existence and uniqueness of positive steady states, local and global stability, persistence, and permanence. We consider the class of disguised toric dynamical systems, which contains toric dynamical systems, and… Expand
2 Citations
The structure of the moduli spaces of toric dynamical systems
We consider complex balanced mass-action systems, also called toric dynamical systems. They are polynomial dynamical systems arising from reaction networks and have remarkable dynamical properties.Expand
Uniqueness of weakly reversible and deficiency zero realization
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Toric dynamical systems
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Persistence and Permanence of Mass-Action and Power-Law Dynamical Systems
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Algebraic methods for biochemical reaction network theory
This dissertation develops the algebraic study of chemical reaction networks endowed with mass-action kinetics, and develops a new method for determining whether given initial concentrations allow for various boundary steady states. Expand
An Efficient Characterization of Complex-Balanced, Detailed-Balanced, and Weakly Reversible Systems
This work describes a computationally efficient characterization of polynomial or power-law dynamical systems that can be obtained as complex- balanced, detailed-balanced, weakly reversible, and reversible mass-action systems. Expand
This article is a survey of the recent use of some techniques from computational algebraic geometry to address mathematical challenges in systems biology. (Bio)chemical reaction networks de neExpand
General mass action kinetics
SummaryThe familiar idea of mass action kinetics is extended to embrace situations more general than chemically reacting mixtures in closed vessels. Thus, for example, many reaction regions connectedExpand
Centennial History of Hilbert’s 16th Problem
The second part of Hilbert’s 16th problem deals with polynomial differential equations in the plane. It remains unsolved even for quadratic polynomials. There were several attempts to solve it thatExpand
Polynomial Dynamical Systems, Reaction Networks, and Toric Differential Inclusions
  • G. Craciun
  • Mathematics, Physics
  • SIAM J. Appl. Algebra Geom.
  • 2019
Some of the most common mathematical models in biology, chemistry, physics, and engineering are polynomial dynamical systems, i.e., systems of differential equations with polynomial right-hand side...
Lower bounds for positive roots and regions of multistationarity in chemical reaction networks
Given a real sparse polynomial system, we present a general framework to find explicit coefficients for which the system has more than one positive solution, based on the recent article by Bihan,Expand