Differential Equations in Biology and Medicine

Data is displayed for the academic year: 2024./2025.

Lecturers

Assoc. Prof.
Domagoj Vlah
PhD
Prof.
Vesna Županović
PhD

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

  1. Explain basic type of differential equations models in biology and neuroscience
  2. Apply methods of nonlinear dynamics
  3. Describe neural network by differential equations

Forms of Teaching

Lectures

Classes

Seminars and workshops

Seminars

Partial e-learning

Online projects

Week by Week Schedule

  1. Bifurcations; Oscillations
  2. Lotka-Volterra predator-prey model
  3. Lotka-Volterra competition model
  4. Slow-fast systems
  5. Mathematical modeling of Hopfield neural network
  6. Modeling Hopfield neural network by differential equations
  7. Modeling Hopfield neural network by delay differential equations, Midterm exam
  8. Midterm exam
  9. Stability of Hopfield network
  10. Hodgkin-Huxley neuronal model
  11. Reaction-diffusion neuronal model of Fitzhugh-Nagumo type
  12. Stability and bifurcations of Fitzhugh-Nagumo system
  13. Reaction–diffusion system in chemistry
  14. Applications to biology and medicine
  15. 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

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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