TY - JOUR

T1 - How to generate species with positive concentrations for all positive times?

AU - Shavarani, Seyed Mahdi

AU - Toth, Janos

AU - Vizvari, Bela

N1 - Funding Information:
JT thanks for the support of the National Research, Development and Innovation Offce (SNN 125739).*%blankline%*
Funding Information:
Acknolwedgmen:tTs hepaperisbasedonatalkgivenbytheauthorsatthe11thConfer-ence on Mathematical and Theoretical Biolog, 23–27y Jul,y2018, Lisboa. Discussions in the friendly and construcetatmosphereiv of the Workshoonp the Adavnceins Chemical ReactionNewtorkTheoryattheErwinSchrödingeInstitue,r Vienna,significtalnycon-tributed to the paper. JT thanks for the support of the National Reseahrc,Developmten and InnvoationOffice (SNN 125739). Careful reading by Prof. Vilmos Gáspa´rand Mr. MihcaeGl ustvaowerealsoagreathelp.
Publisher Copyright:
© 2020 University of Kragujevac, Faculty of Science. All rights reserved.

PY - 2020

Y1 - 2020

N2 - Given a reaction (network) we are looking for minimal sets of species starting from which all the species will have positive concentrations for all positive times in the domain of existence of the solution of the induced kinetic dierential equation. We present three algorithms to solve the problem. The rst one essentially checks all the possible subsets of the sets of species. This can obviously work for only a few dozen species because of combinatorial explosion. The second one is based on an integer programming reformulation of the problem. The third one walks around the state space of the problem in a systematic way and produces all the minimal sets of the advantageous initial species, and works also for large systems. All the algorithms rely heavily on the concept of Volpert indices, used earlier for the decomposition of overall reactions (Kovacs et al., 2004). Relations to the permanence hypothesis, possible economic or medical uses of the solution of the problem are analyzed, and open problems are formulated at the end.

AB - Given a reaction (network) we are looking for minimal sets of species starting from which all the species will have positive concentrations for all positive times in the domain of existence of the solution of the induced kinetic dierential equation. We present three algorithms to solve the problem. The rst one essentially checks all the possible subsets of the sets of species. This can obviously work for only a few dozen species because of combinatorial explosion. The second one is based on an integer programming reformulation of the problem. The third one walks around the state space of the problem in a systematic way and produces all the minimal sets of the advantageous initial species, and works also for large systems. All the algorithms rely heavily on the concept of Volpert indices, used earlier for the decomposition of overall reactions (Kovacs et al., 2004). Relations to the permanence hypothesis, possible economic or medical uses of the solution of the problem are analyzed, and open problems are formulated at the end.

UR - http://www.scopus.com/inward/record.url?scp=85094129328&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85094129328

SN - 0340-6253

VL - 84

SP - 29

EP - 56

JO - Match

JF - Match

IS - 1

ER -