Differential Equations in Biology and Medicine
Data is displayed for academic year: 2023./2024.
Course Description
Dynamical systems. Bifurcations. Discrete and continuous population models.
Lotka-Volterra predator-prey model. Lotka-Volterra competition model.
Slow-fast systems. Modeling Hopfield neural network by differential equations.
Stability of Hopfield network. Bifurcations of Hopfield network.
Hodgkin-Huxley neuronal model. Fitzhugh-Nagumo neuronal model.
Reaction–diffusion equations. Reaction-diffusion models in biochemistry.
Study Programmes
University graduate
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Learning Outcomes
- Explain basic type of differential equations models in biology and neuroscience
- Apply methods of nonlinear dynamics
- Describe neural network by differential equations
Forms of Teaching
Lectures
Classes
Seminars and workshopsSeminars
Partial e-learningOnline projects
Week by Week Schedule
- Bifurcations; Oscillations
- Lotka-Volterra predator-prey model
- Lotka-Volterra competition model
- Slow-fast systems
- Mathematical modeling of Hopfield neural network
- Modeling Hopfield neural network by differential equations
- Modeling Hopfield neural network by delay differential equations, Midterm exam
- Midterm exam
- Stability of Hopfield network
- Hodgkin-Huxley neuronal model
- Reaction-diffusion neuronal model of Fitzhugh-Nagumo type
- Stability and bifurcations of Fitzhugh-Nagumo system
- Reaction–diffusion system in chemistry
- Applications to biology and medicine
- Final exam
Literature
F. Brauer, C. Kribs (2016.), Dynamical systems for biological modeling, An introduction,, Francis Group
G. Bard Ermentrout, D. H. Terman, (20210.), Mathematical Foundations of Neuroscience, Springer
J. D. Murray (2004.), Mathematical Biology, I An introduction, Springer
For students
General
ID 222518
Summer semester
5 ECTS
L1 English Level
L1 e-Learning
45 Lectures
0 Seminar
0 Exercises
0 Laboratory exercises
0 Project laboratory
0 Physical education excercises
Grading System
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