| bibtype |
A -
Abstract
|
| ARLID |
0573178 |
| utime |
20250327191128.8 |
| mtime |
20230623235959.9 |
| title
(primary) (eng) |
Bohl-Marek Formulation of the Nonlinear System of ODEs for a Class of Mathematical Models With Conservation Laws |
| specification |
| page_count |
2 s. |
| media_type |
P |
|
| serial |
| ARLID |
cav_un_epca*0573177 |
| title
|
ODAM 2023 Book of Abstracts |
| page_num |
51-52 |
| publisher |
| place |
Olomouc |
| name |
Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University Olomouc |
| year |
2023 |
|
|
| author
(primary) |
| ARLID |
cav_un_auth*0100790 |
| name1 |
Matonoha |
| name2 |
Ctirad |
| institution |
UIVT-O |
| full_dept (cz) |
Oddělení umělé inteligence |
| full_dept (eng) |
Department of Artificial Intelligence |
| full_dept |
Department of Computational Mathematics |
| fullinstit |
Ústav informatiky AV ČR, v. v. i. |
|
| author
|
| ARLID |
cav_un_auth*0404313 |
| name1 |
Papáček |
| name2 |
Štěpán |
| institution |
UTIA-B |
| full_dept (cz) |
Teorie řízení |
| full_dept |
Department of Control Theory |
| department (cz) |
TŘ |
| department |
TR |
| country |
CZ |
| fullinstit |
Ústav teorie informace a automatizace AV ČR, v. v. i. |
|
| source |
|
| cas_special |
| abstract
(eng) |
Our study presents an application of one special technique, further called the Bohl- Marek formulation, related to the mathematical modeling of biochemical networks with mass conservation properties. Nonlinear cooperative systems possessing certain conservation laws, arising fre- quently in biology and chemistry, were studied by Erich Bohl and Ivo Marek in different papers [1], [2]. The conservation law guarantees a lot of mathematical properties, e.g. the existence and uniqueness results, the positivity of the solutions (for positive inputs), periodicity and controllability, or proposing a stability theorem. These properties are consequence of the fact that the underlying nonlinear dynamical systems describing a class of biochemical networks are built up of linear evolutions with negative M-matrices whose entries depend on the dynamical variables of the other subsystems involved. Thus, the nonlinearity of the whole system is created via this dependence, i.e., the matrix of the complete system is blockwise diagonal. On a case study, namely the Michaelis-Menten enzyme-catalyzed reaction with a substrate transport chain [3], we show how to transform the system of nonlinear ODEs into a set of smaller, quasi-linear subsystems of ODEs with negative M- matrices. For the two model formulations, the classical nonlinear formulation and the quasi-linear Bohl-Marek formulation, we determine and compare the results and show the computational advantages of the latter formulation. |
| action |
| ARLID |
cav_un_auth*0451628 |
| name |
ODAM 2023: Olomoucian Days of Applied Mathematics |
| dates |
20230612 |
| mrcbC20-s |
20230614 |
| place |
Olomouc |
| url |
https://odam.upol.cz/ |
| country |
CZ |
|
| reportyear |
2024 |
| mrcbC52 |
4 O 4o 20231122151408.9 |
| inst_support |
RVO:67985807 |
| inst_support |
RVO:67985556 |
| permalink |
https://hdl.handle.net/11104/0343637 |
| confidential |
S |
| arlyear |
2023 |
| mrcbTft |
\nSoubory v repozitáři: 0573178-aw.pdf |
| mrcbU14 |
SCOPUS |
| mrcbU24 |
PUBMED |
| mrcbU34 |
WOS |
| mrcbU63 |
cav_un_epca*0573177 ODAM 2023 Book of Abstracts Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University Olomouc 2023 Olomouc 51 52 |
|