Multiple Equilibria in Complex Chemical Reaction Networks: I. The Injectivity Property

DOI10.1137/S0036139904440278zbMath1094.80005OpenAlexW1974915811WikidataQ122928722 ScholiaQ122928722MaRDI QIDQ5317463

Gheorghe Craciun, Martin Feinberg

Publication date: 16 September 2005

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0036139904440278

zbMATH Keywords

multiple positive equilibriainjectivity of a reaction network

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Chemical kinetics in thermodynamics and heat transfer (80A30)

Related Items (only showing first 100 items - show all)

Algebraic Perspectives on Signomial Optimization ⋮ Graphical characterizations of robust stability in biological interaction networks ⋮ Structural Conditions for Saddle-Node Bifurcations in Chemical Reaction Networks ⋮ The Disguised Toric Locus and Affine Equivalence of Reaction Networks ⋮ Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry ⋮ An Efficient Characterization of Complex-Balanced, Detailed-Balanced, and Weakly Reversible Systems ⋮ On the Bijectivity of Families of Exponential/Generalized Polynomial Maps ⋮ A Graph-Theoretic Condition for Delay Stability of Reaction Systems ⋮ Multistability of Reaction Networks with One-Dimensional Stoichiometric Subspaces ⋮ Which Small Reaction Networks Are Multistationary? ⋮ Oscillations in biochemical reaction networks arising from pairs of subnetworks ⋮ Injectivity of NURBS curves ⋮ Some consequences of thermodynamic feasibility for chemical reaction networks. Considering thermodynamic feasibility in current CRN research ⋮ Computing the structural influence matrix for biological systems ⋮ Adding species to chemical reaction networks: preserving rank preserves nondegenerate behaviours ⋮ Multistationarity in cyclic sequestration-transmutation networks ⋮ Bistability and oscillations in chemical reaction networks ⋮ Geometric conditions for injectivity of 3D Bézier volumes ⋮ Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems ⋮ Sign patterns for chemical reaction networks ⋮ On the complete integrability of the Raychaudhuri differential system in \(\mathbb {R}^4\) and of a CRNT model in \(\mathbb {R}^5\) ⋮ Computing sparse and dense realizations of reaction kinetic systems ⋮ First-order chemical reaction networks. I: Theoretical considerations ⋮ Necessary and sufficient conditions for protocell growth ⋮ Linear conjugacy in biochemical reaction networks with rational reaction rates ⋮ Critical parameters for singular perturbation reductions of chemical reaction networks ⋮ The role of feedback mechanisms in biological network models-A tutorial ⋮ Structural analysis in biology: a control-theoretic approach ⋮ Polyhedral Lyapunov functions structurally ensure global asymptotic stability of dynamical networks iff the Jacobian is non-singular ⋮ Concordant chemical reaction networks ⋮ A reaction network approach to the theory of acoustic wave turbulence ⋮ Product-form stationary distributions for deficiency zero chemical reaction networks ⋮ Multistationarity in structured reaction networks ⋮ Laplacian dynamics with synthesis and degradation ⋮ Atoms of multistationarity in chemical reaction networks ⋮ Variable elimination in post-translational modification reaction networks with mass-action kinetics ⋮ Solving moment hierarchies for chemical reaction networks ⋮ An improved algorithm for checking the injectivity of 2D toric surface patches ⋮ An algebraic approach to signaling cascades with \(n\) layers ⋮ Chemical reaction network approaches to biochemical systems theory ⋮ Delay stability of reaction systems ⋮ A linear programming approach to weak reversibility and linear conjugacy of chemical reaction networks ⋮ Parametric uniqueness of deficiency zero reaction networks ⋮ A Jacobian criterion for the simultaneous injectivity on positive variables of linearly parameterized polynomial maps ⋮ On classes of reaction networks and their associated polynomial dynamical systems ⋮ The case for algebraic biology: from research to education ⋮ Chemical reaction-diffusion networks: convergence of the method of lines ⋮ Bistability analysis of an apoptosis model in the presence of nitric oxide ⋮ Qualitative analysis of an ODE model of a class of enzymatic reactions. Some results on global stability of messenger RNA-microRNA interaction ⋮ On the existence of the positive steady states of weakly reversible deficiency-one mass action systems ⋮ Reactant subspaces and kinetics of chemical reaction networks ⋮ Weakly Reversible Mass-Action Systems With Infinitely Many Positive Steady States ⋮ A stronger necessary condition for the multistationarity of chemical reaction networks ⋮ Linear conjugacy of chemical reaction networks ⋮ Stochastic switching in biology: from genotype to phenotype ⋮ Turing-Hopf instability in biochemical reaction networks arising from pairs of subnetworks ⋮ On the dependence of the existence of the positive steady states on the rate coefficients for deficiency-one mass action systems: single linkage class ⋮ A graph-theoretical approach for the analysis and model reduction of complex-balanced chemical reaction networks ⋮ Multistationarity in mass action networks with applications to ERK activation ⋮ Translated chemical reaction networks ⋮ On the multistationarity of chemical reaction networks ⋮ Routes to multiple equilibria for mass-action kinetic systems ⋮ A tutorial on chemical reaction network dynamics ⋮ On the stability of metabolic cycles ⋮ Piecewise-linear Lyapunov functions for structural stability of biochemical networks ⋮ Algebra and Geometry in the Study of Enzymatic Cascades ⋮ Regions of multistationarity in cascades of Goldbeter-Koshland loops ⋮ A unified view on bipartite species-reaction graphs and their relation to interaction graphs and qualitative dynamics of chemical reaction networks ⋮ Analyzing multistationarity in chemical reaction networks using the determinant optimization method ⋮ A structural classification of candidate oscillatory and multistationary biochemical systems ⋮ Identifiability of chemical reaction networks ⋮ Graph-theoretic methods for the analysis of chemical and biochemical networks. I. Multistability and oscillations in ordinary differential equation models ⋮ Understanding bistability in complex enzyme-driven reaction networks ⋮ On the Darboux integrability of a cubic CRN model in \(\mathbb R^5\) ⋮ Translation-invariant monotone systems, and a global convergence result for enzymatic futile cycles ⋮ Symbolic analysis of multiple steady states in a MAPK chemical reaction network ⋮ Preclusion of switch behavior in networks with mass-action kinetics ⋮ On the Liouville integrability of Edelstein's reaction system in \(\mathbb R^3\) ⋮ Multi‐equilibrium property of metabolic networks: MMN module ⋮ Monostationarity and multistationarity in tree networks of Goldbeter-Koshland loops ⋮ Methods for and results from the study of design principles in molecular systems ⋮ Finding complex balanced and detailed balanced realizations of chemical reaction networks ⋮ Insufficiency of chemical network model integration using a high-order Taylor series method ⋮ Oscillations in non-mass action kinetics models of biochemical reaction networks arising from pairs of subnetworks ⋮ Some Geometrical Aspects of Control Points for Toric Patches ⋮ Characterizing injectivity of classes of maps via classes of matrices ⋮ Graph-theoretic conditions for injectivity of functions on rectangular domains ⋮ The Smallest Multistationary Mass-Preserving Chemical Reaction Network ⋮ Cycle expansions: from maps to turbulence ⋮ Bistability of sequestration networks ⋮ Some Network Conditions for Positive Recurrence of Stochastically Modeled Reaction Networks ⋮ Homotopy methods for counting reaction network equilibria ⋮ Univalent positive polynomial maps and the equilibrium state of chemical networks of reversible binding reactions ⋮ The number of equilibrium points of perturbed nonlinear positive dynamical systems ⋮ Monotonicity in chemical reaction systems ⋮ Boundedness of a Class of Spatially Discrete Reaction-Diffusion Systems ⋮ Bistable stochastic biochemical networks: highly specific systems with few chemicals ⋮ Steady states and stability in metabolic networks without regulation ⋮ Some Results on Injectivity and Multistationarity in Chemical Reaction Networks ⋮ On necessary and sufficient conditions for proto-cell stationary growth

This page was built for publication: Multiple Equilibria in Complex Chemical Reaction Networks: I. The Injectivity Property