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
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
Grading System
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Sufficient