Скачать или смотреть E340/542 Network Modeling, Lecture 8, Stability Theory [Rita de Almeida] October 22, 2024

ENG340/542 Biological Network Modeling, Lecture 8, Stability in One Dimension with Examples
October 22, 2024
Presented by Prof. Rita de Almeida
Indiana University, Department of Intelligent Systems Engineering and Biocomplexity Institute
Bloomington, IN 47408, USA

Engineering 340/542 teaches how to model network dynamics using the Tellurium/Antimony model specification framework and Python-based Jupyter notebooks. The course covers the basics of developing simple metabolic, cell-signaling, gene-regulatory and pharmaco-kinetic network models and fitting models to experimental data.

Contents
00:00 - Introduction
Review: Stability and Fixed Points in one Dimension
Review: Bifurcations in One Dimension Saddle-Node (Tangent), Transcritical (Exchange of Stability) Bifurcation, Pitchfork (Supercritical) Bifurcation, Inverse Pitchfork (Subcritical Bifurcation)
Review: Workflow for Drawing Null-Cline Plots in Two Dimensions
Exercise 8.1: FitzHugh-Nagumo Equation Excitable State
Exercise 8.2: Fitz-Hugh-Nagumo Equation Oscillatory State
Analysis of Bifurcations in FitzHugh-Nagumo Equation
Theory of Stability in Arbitrary Dimensions
Taylor Expansion in Arbitrary Dimensions
Linearization of the Taylor Expansion
Review of Eigenvalues and Eigenvectors
Exponentiation of Square Matrices
Linear Stability in Higher Dimensions and Relation to Eignevalues of the Jacobean
Trace Lemma
Fundamental Theorem of Stability in Higher Dimensions:
If the real parts of all eigenvalues of the Jacobean are negative, FP is stable
If the real part of ANY eigenvalue of the Jacobean is positive, FP is unstable
Simplification of Stability Theory to Two Dimensions
Exercise 8.3: Rosenzweig-McArthur Model

Slides available at: https://drive.google.com/drive/folder...
Exercises available at: https://drive.google.com/drive/folder...
Demos available at: https://drive.google.com/drive/folder...

For an on-line introduction to the Antimony/Tellurium modeling framework, please see:
https://tellurium.readthedocs.io/en/l...
To download Tellurium visit: https://tellurium.analogmachine.org/

If you found this video useful, please check out our other videos teaching computational modeling:
For dynamic network modeling:    • E340/542 Introduction to Network Modeling ...  
For multicellular agent-based modeling:    • E443/543 Multicell Modeling Spring 2023