Code: 01DRCH Differential Equations and Chaos
Lecturer: prof. Dr. Ing. Michal Beneš Weekly load: 0+2 Completion: A
Department: 14101 Credits: 2 Semester: W
Description:
Basic theorem on the local existence and uniqueness of the solution. Continuous dependence and differentiability of the solution. Basics of the theory of autonomous systems. Analysis of solution of autonomous systems (special solutions, phase space). Exponentials of operators and differential equations. Lyapunov stability. Limit cycles and chaos. Poincaré map. First integrals and integral manifolds. Structural stability and bifurcation. Characteristics of chaotic behaviour.
Contents:
1. Basic theorem on the local existence and uniqueness of the solution
2. Continuous dependence and differentiability of the solution
3. Basics of the theory of autonomous systems
4. Analysis of solution of autonomous systems (special solutions, phase space)
5. Exponentials of operators and differential equations
6. Lyapunov stability
7. Limit cycles and chaos
8. Poincaré map
9. First integrals and integral manifolds
10. Structural stability and bifurcation
11. Characteristics of chaotic behaviour
Seminar contents:
1. Basic theorem on the local existence and uniqueness of the solution
2. Continuous dependence and differentiability of the solution
3. Basics of the theory of autonomous systems
4. Analysis of solution of autonomous systems (special solutions, phase space)
5. Exponentials of operators and differential equations
6. Lyapunov stability
7. Limit cycles and chaos
8. Poincaré map
9. First integrals and integral manifolds
10. Structural stability and bifurcation
11. Characteristics of chaotic behaviour
Recommended literature:
Key references:
[1] M.W.Hirsch, S.Smale, Differential Equations, Dynamical systems, and Linear Algebra, Academic Press, Boston, 1974
[2] F.Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer-Verlag, Berlin 1990
[3] J. Guckenheimer and P.J. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, Berlin 1983

Recommended references:
[3] S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, Berlin 2003
Keywords:
Ordinary differential equations, qualitative theory, parmeter dependence, autonomous systems, limit cycles, Poincaré map

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