Nonlinear systems

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Applied Mathematics

Synopsis:

Model development and parameter identification. Analysis of continuous and discrete non-linear systems. The course presents the solutions of several non-linear models and non-linear differential equations using the software MATLAB and Mathematica. It provides a view of special properties of non-linear systems and their solution: bifurcation, solitary and chaotic phenomena.

Requirements:

Syllabus of lectures:

1.Linear and non-linear systems, continuous and discrete systems, how to form non-linear differential and difference equations.

2.Model development and their classification, examples.

3.Time invariant and time varying dynamic systems.

4.State variables and state variable equations.

5.Special non-linear systems, and special addition property

6.Linear approximation for non-linear models.

7.Numerical integration of non-linear differential equations.

8.Numerical integration of non-linear difference equations.

9.Stability of non-linear system, criteria.

10.Bifurcation, examples.

11.Time invariant periodic solution, synchronisation of periodic systems.

12.Solutions, examples.

13.Surface waves and earthquakes.

14.Almost periodic solutions, chaotic solutions.

Syllabus of tutorials:

Study Objective:

Study materials:

Sastry S.: Nonlinear Systems Analysis, Stability and Control, Springer Verlag, 1999

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: