| Title |
Graph-theoretic methods for the analysis of chemical and biochemical networks. I. Multistability and oscillations in ordinary differential equation models
|
|---|---|
| Published in |
Journal of Mathematical Biology, May 2007
|
| DOI | 10.1007/s00285-007-0099-1 |
| Pubmed ID | |
| Authors |
Maya Mincheva, Marc R. Roussel |
| Abstract |
A chemical mechanism is a model of a chemical reaction network consisting of a set of elementary reactions that express how molecules react with each other. In classical mass-action kinetics, a mechanism implies a set of ordinary differential equations (ODEs) which govern the time evolution of the concentrations. In this article, ODE models of chemical kinetics that have the potential for multiple positive equilibria or oscillations are studied. We begin by considering some methods of stability analysis based on the digraph of the Jacobian matrix. We then prove two theorems originally given by A. N. Ivanova which correlate the bifurcation structure of a mass-action model to the properties of a bipartite graph with nodes representing chemical species and reactions. We provide several examples of the application of these theorems. |
Mendeley readers
The data shown below were compiled from readership statistics for 66 Mendeley readers of this research output. Click here to see the associated Mendeley record.
Geographical breakdown
| Country | Count | As % |
|---|---|---|
| United States | 3 | 5% |
| Colombia | 1 | 2% |
| Germany | 1 | 2% |
| Hungary | 1 | 2% |
| Canada | 1 | 2% |
| Austria | 1 | 2% |
| Spain | 1 | 2% |
| Belgium | 1 | 2% |
| Unknown | 56 | 85% |
Demographic breakdown
| Readers by professional status | Count | As % |
|---|---|---|
| Student > Ph. D. Student | 18 | 27% |
| Researcher | 17 | 26% |
| Student > Master | 9 | 14% |
| Professor | 4 | 6% |
| Student > Doctoral Student | 3 | 5% |
| Other | 10 | 15% |
| Unknown | 5 | 8% |
| Readers by discipline | Count | As % |
|---|---|---|
| Agricultural and Biological Sciences | 14 | 21% |
| Biochemistry, Genetics and Molecular Biology | 9 | 14% |
| Mathematics | 9 | 14% |
| Engineering | 7 | 11% |
| Computer Science | 6 | 9% |
| Other | 10 | 15% |
| Unknown | 11 | 17% |
Attention Score in Context
This research output has an Altmetric Attention Score of 3. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 29 August 2012.
All research outputs
#12,861,953
of 22,681,577 outputs
Outputs from Journal of Mathematical Biology
#245
of 654 outputs
Outputs of similar age
#58,998
of 70,698 outputs
Outputs of similar age from Journal of Mathematical Biology
#3
of 3 outputs
Altmetric has tracked 22,681,577 research outputs across all sources so far. This one is in the 42nd percentile – i.e., 42% of other outputs scored the same or lower than it.
So far Altmetric has tracked 654 research outputs from this source. They receive a mean Attention Score of 3.6. This one has gotten more attention than average, scoring higher than 61% of its peers.
Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 70,698 tracked outputs that were published within six weeks on either side of this one in any source. This one is in the 16th percentile – i.e., 16% of its contemporaries scored the same or lower than it.
We're also able to compare this research output to 3 others from the same source and published within six weeks on either side of this one.