Nonlinear dynamics and stochastic processes (Nichtlineare Dynamik und stochastische Prozesse)

Wahllehrveranstaltung 3233 L 505 im Wintersemester 2016/17

Dozent: Dr. Anna Zakharova, anna.zakharova@tu-berlin.de [1]

Vorlesung:
Mi 10:15-11:45 EW 733 (Beginn 19.10.)

Für Studierende der Physik (Master), Mathematik (Master) und anderer naturwissenschaftlicher Masterstudiengänge und interessierte Mitglieder des SFB 910.

When attending this course 3 credit points within the ECTS system can be obtained. The course will be given in English.

Zusammen mit der Lehrveranstaltung LV 3232 L 120 „Theoretische Physik VI (Vertiefung): Nichtlineare Dynamik und Kontrolle"(zuletzt gelesen im SS 2016)  kann diese Vorlesung auch zu einem physikalischen Wahlpflichtmodul (8 SWS)  mit 12 ECTS kombiniert werden.

Außerdem gibt es in diesem Semester ein ergänzendes Seminar zum Thema "Control of Complex Systems and Networks [2]".

The lectures cover the main concepts of nonlinear dynamics, emphasizing characterization of stochastic systems, i.e. nonlinear systems in the presence of random fluctuations. First, the basic ideas of nonlinear dynamics, such as characterization of deterministic nonlinear systems, stability analysis, bifurcations and attractors will be introduced. Further, the main concepts of the theory of stochastic processes will be explained. A special attention will be paid to synchronization and bifurcations in the presence of noise. We will consider the most prominent examples of noise-induced effects, such as stochastic resonance and coherence resonance. These phenomena provide the evidence for constructive counter-intuitive role of random fluctuations in dynamical systems. They will be illustrated by examples from biology and climate. Finally, selected parts of complex networks theory will be presented with a special focus on collective behavior of coupled elements in the presence of random fluctuations. Various applications in different fields of science including physics, chemistry, biology and engineering will be discussed. More specifically, the following topics will be discussed in the lectures:

 

• deterministic and stochastic nonlinear systems

• bifurcations in the presence of random fluctuations

• noisy periodic and deterministic chaotic dynamics

• synchronization of stochastic systems

• Fokker-Planck and Langevin equations

• stochastic resonance

• coherence resonance

• control by means of noise

• noise effects in complex networks

19.10.16 Introduction [3]

26.10.16 Stability Analysis [4]

02.11.16 Deterministic Bifurcations [5]

09.11.16 Stochastic Bifurcations [6]

16.11.16 Basic concepts of stochastic dynamics [7]

23.11.16 Moments of stochastic processes [8]

30.11.16 Fokker-Planck Equation [9]

07.12.16 Fokker-Planck versus Langevin [10]

14.12.16 Fokker-Planck versus Langevin (2) [11]

04.01.17 Coherence resonance [12]

11.01.17 Coherence resonance in nonexcitable systems [13]

18.01.17 Synthetic gene oscillator [14]

25.01.17 Stochastic resonance [15]

01.02.17 Amplitude and phase description [16]

08.02.17 Synchronization [17]

15.02.17 Effective synchronization [18]

Books:

• S. Strogatz, Nonlinear Dynamics and Chaos: With Applications To Physics Biology, Chemistry And Engineering, Westview Press (2000)
• Anishchenko, V. S., Astakhov, V., Neiman, A. B., Vadivasova, T. and Schimansky-Geier, L., Nonlinear dynamics of chaotic and stochastic systems: tutorial and modern developments, Springer (2007)