A Survey of Methods for Deciding Whether a Reaction Network is Multistationary
Math. Model. Nat. Phenom., 10 5 (2015) 47-67
Published online: 2015-08-27
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
The Generic Geometry of Steady State Varieties
Elisenda Feliu, Oskar Henriksson and Beatriz Pascual-EscuderoSIAM Journal on Applied Algebra and Geometry 10 (3) 519 (2026)
https://doi.org/10.1137/25M1731289
Computing positive tropical varieties and lower bounds on the number of positive roots
Kemal Rose and Máté L. TelekJournal of Symbolic Computation 132 102477 (2026)
https://doi.org/10.1016/j.jsc.2025.102477
Routing Functions for Parameter Space Decomposition to Describe Stability Landscapes of Ecological Models
Joseph Cummings, Kyle J.-M. Dahlin, Elizabeth Gross and Jonathan D. HauensteinBulletin of Mathematical Biology 87 (12) (2025)
https://doi.org/10.1007/s11538-025-01554-7
Mixed volumes of networks with binomial steady-states
Jane Ivy Coons, Maize Curiel and Elizabeth GrossJournal of Symbolic Computation 128 102395 (2025)
https://doi.org/10.1016/j.jsc.2024.102395
Rigorously proven chaos in chemical kinetics
M. Susits and J. TóthChaos: An Interdisciplinary Journal of Nonlinear Science 34 (10) (2024)
https://doi.org/10.1063/5.0206749
Newton-Okounkov bodies of chemical reaction systems
Nida Kazi Obatake and Elise WalkerAdvances in Applied Mathematics 155 102672 (2024)
https://doi.org/10.1016/j.aam.2024.102672
On the connectedness of multistationarity regions of small reaction networks
Allison McClure and Anne ShiuJournal of Symbolic Computation 125 102323 (2024)
https://doi.org/10.1016/j.jsc.2024.102323
Deficiency of chemical reaction networks: the effect of operations that preserve multistationarity and periodic orbits
Awildo Gutierrez, Elijah Leake, Caelyn Rivas-Sobie, Jordy Lopez Garcia and Anne ShiuDiscrete and Continuous Dynamical Systems - B (2024)
https://doi.org/10.3934/dcdsb.2024157
An Algorithm for Finding Weakly Reversible Deficiency Zero Realizations of Polynomial Dynamical Systems
Gheorghe Craciun, Jiaxin Jin and Polly Y. YuSIAM Journal on Applied Mathematics 83 (4) 1717 (2023)
https://doi.org/10.1137/22M1499558
The Disguised Toric Locus and Affine Equivalence of Reaction Networks
Sabina J. Haque, Matthew Satriano, Miruna–Ştefana Sorea and Polly Y. YuSIAM Journal on Applied Dynamical Systems 22 (2) 1423 (2023)
https://doi.org/10.1137/22M149853X
Topological descriptors of the parameter region of multistationarity: Deciding upon connectivity
Máté László Telek, Elisenda Feliu and Jason M. HaughPLOS Computational Biology 19 (3) e1010970 (2023)
https://doi.org/10.1371/journal.pcbi.1010970
Nonlinear algebra and applications
Paul Breiding, Türkü Özlüm Çelik, Timothy Duff, et al.Numerical Algebra, Control and Optimization 13 (1) 81 (2023)
https://doi.org/10.3934/naco.2021045
Reaction Network Motifs for Static and Dynamic Absolute Concentration Robustness
Badal Joshi and Gheorghe CraciunSIAM Journal on Applied Dynamical Systems 22 (2) 501 (2023)
https://doi.org/10.1137/22M1476162
Power-Engine-Load Form for Dynamic Absolute Concentration Robustness
Badal Joshi and Gheorghe CraciunSIAM Journal on Applied Mathematics 83 (6) 2237 (2023)
https://doi.org/10.1137/22M1535450
Prevalence of Multistationarity and Absolute Concentration Robustness in Reaction Networks
Badal Joshi, Nidhi Kaihnsa, Tung D. Nguyen and Anne ShiuSIAM Journal on Applied Mathematics 83 (6) 2260 (2023)
https://doi.org/10.1137/23M1549316
Homeostasis and injectivity: a reaction network perspective
Gheorghe Craciun and Abhishek DeshpandeJournal of Mathematical Biology 85 (6-7) (2022)
https://doi.org/10.1007/s00285-022-01795-3
Critical Parameters for Singular Perturbation Reductions of Chemical Reaction Networks
Elisenda Feliu, Sebastian Walcher and Carsten WiufJournal of Nonlinear Science 32 (6) (2022)
https://doi.org/10.1007/s00332-022-09843-4
On generalizing Descartes' rule of signs to hypersurfaces
Elisenda Feliu and Máté L. TelekAdvances in Mathematics 408 108582 (2022)
https://doi.org/10.1016/j.aim.2022.108582
A Geometric Approach for Analyzing Parametric Biological Systems by Exploiting Block Triangular Structure
Changbo Chen and Wenyuan WuSIAM Journal on Applied Dynamical Systems 21 (2) 1573 (2022)
https://doi.org/10.1137/21M1436373
Foundations of static and dynamic absolute concentration robustness
Badal Joshi and Gheorghe CraciunJournal of Mathematical Biology 85 (5) (2022)
https://doi.org/10.1007/s00285-022-01823-2
Multistationarity in Cyclic Sequestration-Transmutation Networks
Gheorghe Craciun, Badal Joshi, Casian Pantea and Ike TanBulletin of Mathematical Biology 84 (6) (2022)
https://doi.org/10.1007/s11538-022-01021-7
Symbolic Proof of Bistability in Reaction Networks
Angélica Torres and Elisenda FeliuSIAM Journal on Applied Dynamical Systems 20 (1) 1 (2021)
https://doi.org/10.1137/20M1326672
The steady-state degree and mixed volume of a chemical reaction network
Elizabeth Gross and Cvetelina HillAdvances in Applied Mathematics 131 102254 (2021)
https://doi.org/10.1016/j.aam.2021.102254
Dynamic bistable switches enhance robustness and accuracy of cell cycle transitions
Jan Rombouts, Lendert Gelens and Attila Csikász-NagyPLOS Computational Biology 17 (1) e1008231 (2021)
https://doi.org/10.1371/journal.pcbi.1008231
Goal Directedness, Chemical Organizations, and Cybernetic Mechanisms
Evo Busseniers, Tomas Veloz and Francis HeylighenEntropy 23 (8) 1039 (2021)
https://doi.org/10.3390/e23081039
Structural analysis in biology: A control-theoretic approach
Franco Blanchini and Giulia GiordanoAutomatica 126 109376 (2021)
https://doi.org/10.1016/j.automatica.2020.109376
Autocatalytic Networks: An Intimate Relation between Network Topology and Dynamics
Badal Joshi and Gheorghe CraciunSIAM Journal on Applied Mathematics 81 (4) 1623 (2021)
https://doi.org/10.1137/20M1342720
Mixed volume of small reaction networks
Nida Obatake, Anne Shiu and Dilruba SofiaInvolve, a Journal of Mathematics 13 (5) 845 (2020)
https://doi.org/10.2140/involve.2020.13.845
Joining and decomposing reaction networks
Elizabeth Gross, Heather Harrington, Nicolette Meshkat and Anne ShiuJournal of Mathematical Biology 80 (6) 1683 (2020)
https://doi.org/10.1007/s00285-020-01477-y
Inverse Population Balance Problems: Heuristics for Aggregation/Breakage of Solid Clusters in Liquid Metals
Jean-Marc Auger, Sylvain Martin and Frédéric GruyIndustrial & Engineering Chemistry Research 59 (22) 10373 (2020)
https://doi.org/10.1021/acs.iecr.0c00859
Coloured Noise from Stochastic Inflows in Reaction–Diffusion Systems
Michael F. Adamer, Heather A. Harrington, Eamonn A. Gaffney and Thomas E. WoolleyBulletin of Mathematical Biology 82 (4) (2020)
https://doi.org/10.1007/s11538-020-00719-w
Systems of polynomials with at least one positive real zero
Jie WangJournal of Algebra and Its Applications 19 (10) 2050183 (2020)
https://doi.org/10.1142/S0219498820501832
Families of toric chemical reaction networks
Michael F. Adamer and Martin HelmerJournal of Mathematical Chemistry 58 (9) 2061 (2020)
https://doi.org/10.1007/s10910-020-01162-x
(2020)
https://doi.org/10.1101/2020.08.11.246017
Identifying the parametric occurrence of multiple steady states for some biological networks
Russell Bradford, James H. Davenport, Matthew England, Hassan Errami, Vladimir Gerdt, Dima Grigoriev, Charles Hoyt, Marek Košta, Ovidiu Radulescu, Thomas Sturm and Andreas WeberJournal of Symbolic Computation 98 84 (2020)
https://doi.org/10.1016/j.jsc.2019.07.008
Addition of flow reactions preserving multistationarity and bistability
Daniele Cappelletti, Elisenda Feliu and Carsten WiufMathematical Biosciences 320 108295 (2020)
https://doi.org/10.1016/j.mbs.2019.108295
Programming Multistationarity in Chemical Replication Networks
Nathaniel Wagner, Rakesh Mukherjee, Indrajit Maity, Sagi Kraun and Gonen AshkenasyChemSystemsChem 2 (2) (2020)
https://doi.org/10.1002/syst.201900048
Delay stability of reaction systems
Gheorghe Craciun, Maya Mincheva, Casian Pantea and Polly Y. YuMathematical Biosciences 326 108387 (2020)
https://doi.org/10.1016/j.mbs.2020.108387
Multistationarity in Structured Reaction Networks
Alicia Dickenstein, Mercedes Pérez Millán, Anne Shiu and Xiaoxian TangBulletin of Mathematical Biology 81 (5) 1527 (2019)
https://doi.org/10.1007/s11538-019-00572-6
Complexity of model testing for dynamical systems with toric steady states
Michael F. Adamer and Martin HelmerAdvances in Applied Mathematics 110 42 (2019)
https://doi.org/10.1016/j.aam.2019.06.001
Monostationarity and Multistationarity in Tree Networks of Goldbeter–Koshland Loops
Alexander Barabanschikov and Jeremy GunawardenaBulletin of Mathematical Biology 81 (7) 2463 (2019)
https://doi.org/10.1007/s11538-019-00615-y
Oscillations and bistability in a model of ERK regulation
Nida Obatake, Anne Shiu, Xiaoxian Tang and Angélica TorresJournal of Mathematical Biology 79 (4) 1515 (2019)
https://doi.org/10.1007/s00285-019-01402-y
279 (2019)
https://doi.org/10.1016/B978-0-12-814066-6.00009-X
Multistationarity and Bistability for Fewnomial Chemical Reaction Networks
Elisenda Feliu and Martin HelmerBulletin of Mathematical Biology 81 (4) 1089 (2019)
https://doi.org/10.1007/s11538-018-00555-z
(2019)
https://doi.org/10.1101/731018
Inferring reaction network structure from single-cell, multiplex data, using toric systems theory
Shu Wang, Jia-Ren Lin, Eduardo D. Sontag, Peter K. Sorger and Pedro MendesPLOS Computational Biology 15 (12) e1007311 (2019)
https://doi.org/10.1371/journal.pcbi.1007311
The Inheritance of Nondegenerate Multistationarity in Chemical Reaction Networks
Murad Banaji and Casian PanteaSIAM Journal on Applied Mathematics 78 (2) 1105 (2018)
https://doi.org/10.1137/16M1103506
Mathematical Analysis of Chemical Reaction Systems
Polly Y. Yu and Gheorghe CraciunIsrael Journal of Chemistry 58 (6-7) 733 (2018)
https://doi.org/10.1002/ijch.201800003
Reaction Kinetics: Exercises, Programs and Theorems
János Tóth, Attila László Nagy and Dávid PappReaction Kinetics: Exercises, Programs and Theorems 115 (2018)
https://doi.org/10.1007/978-1-4939-8643-9_7
Dynamics of Posttranslational Modification Systems: Recent Progress and Future Directions
Carsten Conradi and Anne ShiuBiophysical Journal 114 (3) 507 (2018)
https://doi.org/10.1016/j.bpj.2017.11.3787
45 (2017)
https://doi.org/10.1145/3087604.3087622
Flows, scaling, and the control of moment hierarchies for stochastic chemical reaction networks
Eric Smith and Supriya KrishnamurthyPhysical Review E 96 (6) (2017)
https://doi.org/10.1103/PhysRevE.96.062102
Bistability and Bifurcation in Minimal Self‐Replication and Nonenzymatic Catalytic Networks
Nathaniel Wagner, Rakesh Mukherjee, Indrajit Maity, Enrique Peacock‐Lopez and Gonen AshkenasyChemPhysChem 18 (13) 1842 (2017)
https://doi.org/10.1002/cphc.201601293
Solving moment hierarchies for chemical reaction networks
Supriya Krishnamurthy and Eric SmithJournal of Physics A: Mathematical and Theoretical 50 (42) 425002 (2017)
https://doi.org/10.1088/1751-8121/aa89d0
Which Small Reaction Networks Are Multistationary?
Badal Joshi and Anne ShiuSIAM Journal on Applied Dynamical Systems 16 (2) 802 (2017)
https://doi.org/10.1137/16M1069705
Identifying parameter regions for multistationarity
Carsten Conradi, Elisenda Feliu, Maya Mincheva, Carsten Wiuf and Philip K MainiPLOS Computational Biology 13 (10) e1005751 (2017)
https://doi.org/10.1371/journal.pcbi.1005751
Computer Algebra in Scientific Computing
Matthew England, Hassan Errami, Dima Grigoriev, et al.Lecture Notes in Computer Science, Computer Algebra in Scientific Computing 10490 93 (2017)
https://doi.org/10.1007/978-3-319-66320-3_8
Analyzing multistationarity in chemical reaction networks using the determinant optimization method
Bryan Félix, Anne Shiu and Zev WoodstockApplied Mathematics and Computation 287-288 60 (2016)
https://doi.org/10.1016/j.amc.2016.04.030
Dynamical Systems on Networks
Mason A. Porter and James P. GleesonFrontiers in Applied Dynamical Systems: Reviews and Tutorials, Dynamical Systems on Networks 4 29 (2016)
https://doi.org/10.1007/978-3-319-26641-1_4