Related Experiment Video
Updated: Jul 14, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
Published on: December 7, 2021
Graph-theoretic methods for the analysis of chemical and biochemical networks. I. Multistability and oscillations in
Maya Mincheva1, Marc R Roussel
1Department of Chemistry and Biochemistry, University of Lethbridge, Lethbridge, Alberta, Canada. mincheva@math.wisc.edu
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.
Related Concept Videos
Fundamental Mathematical Principles in Pharmacokinetics: Calculus and Graphs
On the other hand, integral calculus focuses on...
Modeling with Differential Equations
Multimachine Stability
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
Classification of Systems-II
Pharmacokinetic Models: Overview
There are three primary types of models: empirical, compartment, and physiological. Empirical models, with minimal assumptions,...
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
