M6VM06 Deterministic models

Faculty of Science
Spring 2008 - for the purpose of the accreditation
Extent and Intensity
2/1. 5 credit(s). Type of Completion: k (colloquium).
Teacher(s)
doc. RNDr. Lenka Přibylová, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Lenka Přibylová, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The aim is to make students acquainted with methods of deterministic modelling. At the end of the course students should be able to construct and make computer simulation of a process from a chosen area.
Syllabus
  • basic concepts: object, system, model, vazby; state variables, transition equations, constraining conditions, static and dynamic model.
  • Software: Maple, MapleSim, MATLAB, XppAut, table processors.
  • Static models, comparative statics
  • Static graph model - phylogenetic trees.
  • Dynamic models - discrete a continuous models, linear and nonlinear models, structured models
  • Basic continuous and discrete models of growth - exponential and logistic growth
  • Structured discrete dynamic model: Leslie-Lefkovitch models of population growth
  • Structured continuous dynamic model: epidemiologic models
  • Models of interactions - models of predation, competition and mutualism
  • Model of diffusion and taxis - chemical, biological (models of invasion, tumor growth) and economic applications (Bass model of innovation)
  • Evolution games - models of symmetric and asymmetric conflicts
  • Cellular automata - "life game"
Literature
  • KULENOVIĆ, Mustafa R. S. and Orlando MERINO. Discrete dynamical systems and difference equations with Mathematica. Boca Raton, Fla.: Chapman & Hall/CRC, 2002, xv, 344 s. ISBN 1-58488-287-5. info
  • LYNCH, Stephen. Dynamical systems with applications using MAPLE. Boston: Birkhäuser, 2000, xiii, 398. ISBN 0-8176-4150-5. info
Teaching methods (in Czech)
V přednášce budou studenti seznámeni s nutným matematickým minimem pro porozumění jednotlivým technikám modelování. Ty nebudou hlouběji teoreticky analyzovány, ale ve cvičení na konkrétních modelech známých z přírodních věd nebo ekonomie rozvíjeny a ilustrovány. Předpokladem k udělení kolokvia je samostatné (případně ve spolupráci menší skupiny) vytvoření modelu z vybrané oblasti a jeho implementace na počítači.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms spring 2012 - acreditation, Spring 2013, Spring 2015, Spring 2017, Spring 2019, Spring 2021.