Lecture: Dynamical systems with hysteresis (MA5905)
Prof. Dr. Sergey Tikhomirov ^{},Infos
- Time and Place: Vorlesung: Dienstag von 12:15-13:45 Uhr und Donnerstag von 10:15-11:45 Uhr in MI 03.04.011
- Language: Englisch
Content
Hysteresis operator naturally appears in control theory and as a mechanism of self-organisation.If we want to have in the room temperature +20 degrees the mostly used strategy is to choose two thresholds +19 and +21 and turn on/turn off the heating device by the following strategy: when temperature in the room reaches +19 we turn on heating, and when temperature reaches +21 we turn off heating. The mathematical description of such «decisions» is non-ideal relay – the simplest form of hysteresis.
The main features of systems with hysteresis are the dependence of the output on the prehistory of the input, rate independence, and nonsmoothness. Hysteresis operators are applied in mathematical descriptions of various physical, chemical and biological processes: thermocontrol, chemical reactors, ferro-magnetism, self-organisation and others.
In the course we consider dynamical processes involving hysteresis operators. We start from basics.
The topics include the following:
- Examples of hysteresis
- Discontinuous differential equations
- Discontinuous and continuous hysteresis operators
- Differential equations with hysteresis
- Periodic solutions
- Stability of solutions
- Chaos in systems with hysteresis
- Relation to systems acting on several times scales
- Hysteresis and Machine Learning
- Spatially-distributed hysteresis