Routes to Multiple Equilibria for Mass-Action Kinetic Systems
In this work we explore two potential mechanisms inducing multiple equilibria for weakly reversible networks with mass-action kinetics. The study is performed on a class of polynomial dynamic systems that, under some mild assumptions, are able to accommodate in their state-space form weakly reversib...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/3912627 |
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| author | Antonio A. Alonso Irene Otero-Muras Manuel Pájaro |
| author_facet | Antonio A. Alonso Irene Otero-Muras Manuel Pájaro |
| author_sort | Antonio A. Alonso |
| collection | DOAJ |
| description | In this work we explore two potential mechanisms inducing multiple equilibria for weakly reversible networks with mass-action kinetics. The study is performed on a class of polynomial dynamic systems that, under some mild assumptions, are able to accommodate in their state-space form weakly reversible mass-action kinetic networks. The contribution is twofold. We provide an explicit representation of the set of all positive equilibria attained by the system class in terms of a set of (positive parameter dependent) algebraic relations. With this in hand, we prove that deficiency-one networks can only admit multiple equilibria via folding of the equilibrium manifold, whereas a bifurcation leading to multiple branches is only possible in networks with deficiencies larger than one. Interestingly, some kinetic networks within this latter class are capable of sustaining multiple equilibria for any reaction simplex, as we illustrate with one example. |
| format | Article |
| id | doaj-art-26e73c4485e340b5b7ec7e1d03dbe41b |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-26e73c4485e340b5b7ec7e1d03dbe41b2025-02-03T01:24:04ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/39126273912627Routes to Multiple Equilibria for Mass-Action Kinetic SystemsAntonio A. Alonso0Irene Otero-Muras1Manuel Pájaro2BioProcess Engineering Group, IIM-CSIC, Spanish National Research Council, Eduardo Cabello 6, 36208, Vigo, SpainBioProcess Engineering Group, IIM-CSIC, Spanish National Research Council, Eduardo Cabello 6, 36208, Vigo, SpainBioProcess Engineering Group, IIM-CSIC, Spanish National Research Council, Eduardo Cabello 6, 36208, Vigo, SpainIn this work we explore two potential mechanisms inducing multiple equilibria for weakly reversible networks with mass-action kinetics. The study is performed on a class of polynomial dynamic systems that, under some mild assumptions, are able to accommodate in their state-space form weakly reversible mass-action kinetic networks. The contribution is twofold. We provide an explicit representation of the set of all positive equilibria attained by the system class in terms of a set of (positive parameter dependent) algebraic relations. With this in hand, we prove that deficiency-one networks can only admit multiple equilibria via folding of the equilibrium manifold, whereas a bifurcation leading to multiple branches is only possible in networks with deficiencies larger than one. Interestingly, some kinetic networks within this latter class are capable of sustaining multiple equilibria for any reaction simplex, as we illustrate with one example.http://dx.doi.org/10.1155/2018/3912627 |
| spellingShingle | Antonio A. Alonso Irene Otero-Muras Manuel Pájaro Routes to Multiple Equilibria for Mass-Action Kinetic Systems Complexity |
| title | Routes to Multiple Equilibria for Mass-Action Kinetic Systems |
| title_full | Routes to Multiple Equilibria for Mass-Action Kinetic Systems |
| title_fullStr | Routes to Multiple Equilibria for Mass-Action Kinetic Systems |
| title_full_unstemmed | Routes to Multiple Equilibria for Mass-Action Kinetic Systems |
| title_short | Routes to Multiple Equilibria for Mass-Action Kinetic Systems |
| title_sort | routes to multiple equilibria for mass action kinetic systems |
| url | http://dx.doi.org/10.1155/2018/3912627 |
| work_keys_str_mv | AT antonioaalonso routestomultipleequilibriaformassactionkineticsystems AT ireneoteromuras routestomultipleequilibriaformassactionkineticsystems AT manuelpajaro routestomultipleequilibriaformassactionkineticsystems |