Differential Equations in Biology and Medicine

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.

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

Seminars and workshops

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

Study Programmes

University graduate
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Literature

(.), • F. Brauer, C. Kribs, Dynamical systems for biological modeling, An introduction, Taylor & Francis Group 2016 ,
(.), G. Bard Ermentrout, D. H. Terman, Mathematical Foundations of Neuroscience, Springer 2010,
(.), J. D. Murray, Mathematical Biology, I An introduction, Springer 2004.,

Associate Lecturers

For students

General

ID 222518
  Summer semester
5 ECTS
L3 English Level
L1 e-Learning
45 Lectures