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Mihály Pituk, professor

Topics covered:

Continuous semidynamical and dynamical systems, basic properties. Invariance, limit sets, stability. Motions in metric spaces Lyapunov stability, periodic and almost periodic orbits. Ordinary differential equations as dynamical systems. Qualitative properties of monotone dynamical systems. Cooperative functional-differential equations. Examples from the topic of biochemical regulatory circuits, neural networks, transport processes, and population models.
General theory of discrete dynamical systems. Qualitative properties of difference equations. Periodic solutions, bifurcation, chaos, oscillation. Unified theory of continuous and discrete dynamical systems: time-scale calculus. Asymptotic properties of solutions. Difference equations in population dynamics, discrete control systems, economical models.


V.I. Arnold, Közönséges differenciálegyenletek, Műszaki Könyvkiadó, Budapest, 1987.
N. Rouche, P. Habets, M. Laloy, Stability Theory by Liapunov’s Direct Method, Műszaki Springer-Verlag New York, 1977.
S.H. Saperstone, Semidynamical systems in infinite dimensional spaces, Springer-Verlag, New York, Heidelberg, Berlin, 1981.
H.L. Smith, Monotone dynamical systems, An introduction to the theory of competitive and cooperative systems, American Mathematical Society, Providence, Rhode Island, 1995.