MATHEON Junior Research Group in Applied Mathematics "Dynamics and synchronization of complex systems"

Group members:

PD Dr.sc. Serhiy Yanchuk (head)	MATHEON		2093 - 5435 (2.109)
PD Dr.hab. Michael Zaks	MATHEON		2093 - 2317 (2.115)
Leonhard Lücken	SFB910		2093 - 5432 (2.101)
Markus Kantner	SFB910
Jan Philipp Pade	IGK1740		2093 - 5432 (2.101)
Petar Tomov	IGK1740		2093 - 2317 (2.115)
t.b.a.	IGK1740

Former members:

Institute of Mathematics, Humboldt University of Berlin. 

Research Interests:

• Dynamics of coupled systems, networks, synchronization phenomena
  
• Systems with delay
  
• Nonlinear dynamics in general
  
• Applications to laser dynamics and other fields
  

MATHEON Project D21 (started June 2008): Synchronization phenomena in coupled dynamical systems

The cooperative behavior of coupled nonlinear oscillators is significant to a wide variety of physical, technical and biological processes. In arrays of semiconductor lasers, for instance, a variety of dynamical regimes appear due to the coupling of different active and passive elements. Such regimes include self-pulsations, mode-locked pulsations, frequency oscillations, chaotic oscillations and their synchronization, etc.
The goal of this project is to study experimentally relevant aspects of the dynamics of coupled opto-electronic systems. Among numerous open problems in this field, one can mention the following: effect of large delayed feedback on the dynamics of semiconductor lasers, amplitude synchronization in coupled semiconductor lasers, effect of external quasiperiodic perturbations on the dynamics of a nonstationary laser, time-delayed feedback control of multisection semiconductor lasers, and others.
Besides the application field semiconductor lasers, we would like to use the synergy effects by extending the application range and applying the obtained theoretical results to neural systems.

Publications in Refereed Journals starting from 2008

1. M. Lichtner, M. Wolfrum, S. Yanchuk. The spectrum of delay differential equations with large delay, SIAM J. Math. Anal. 43, pp. 788-802 (2011). (preprint)
2. Michael A. Zaks. On chaotic subthreshold oscillations in a simple neuronal model. Mathematical Modelling of Natural Phenomena, 6:149-162, 2011.
3. Michael A. Zaks and Denis S. Goldobin. Comment on "time-averaged properties of unstable periodic orbits and chaotic orbits in ordinary dierential equation systems". Phys Rev E, 81(1 Pt 2):018201; discussion 018202, 2010.
   
4. L. Lücken and S. Yanchuk,  Two-cluster bifurcations in systems of globally pulse-coupled oscillators, Physica D 241 350–359 (2012) 
5. O. Popovych, S. Yanchuk and P. Tass, Delay- and coupling-induced firing patterns in oscillatory neural loops, Phys. Rev. Lett. 107, 228102 (2011), PDF
6. S. Heiligenthal, Th. Dahms, S. Yanchuk, Th. Jüngling, V. Flunkert, I. Kanter, E. Schöll, W. Kinzel, Strong and weak chaos in nonlinear networks with time-delayed couplings, Phys. Rev. Lett. 107, 234102 (2011)
7. S. Yanchuk, P. Perlikowski, O. Popovych, P. Tass, Variability of spatio-temporal patterns in non-homogeneous rings of spiking neurons, Chaos 21, 047511 (2011) PDF
8. M. Wolfrum, O. E. Omel'chenko, S. Yanchuk, and Y. L. Maistrenko, Spectral properties of chimera states, Chaos 21, 013112 (2011); PDF.
9. M. Wolfrum, S. Yanchuk, P. Hövel and E. Schöll,  Complex dynamics in delay-differential equations with large delay, Eur. Phys. J. Special Topics 191, 91–103 (2010) (PDF)
10. V. Flunkert, S. Yanchuk, T. Dahms, E. Schöll, Synchronizing distant nodes: a universal classification of networks, Phys. Rev. Lett. 105, 254101 (2010) (PDF).
11. P. Perlikowski, S. Yanchuk, P. A. Tass, O. V. Popovych. Periodic patterns in a ring of delay-coupled oscillators,  Phys. Rev. E. 82, 036208 (2010) (PDF)
    
12. L. Recke, A. Samoilenko, A. Teplinsky, V. Tkachenko, and S. Yanchuk. Frequency locking of modulated waves.  Discrete and continuous Dynamical Systems - A (accepted in 2010). ArXiv preprint.
13. P. Perlikowski, S. Yanchuk, M. Wolfrum, A. Stefanski, P. Mosiolek, and T. Kapitaniak, Routes to complex dynamics in a ring of unidirectionally coupled systems. Chaos, 20, 013111 (2010) (PDF)
14. S. Yanchuk and M. Wolfrum. A multiple timescale approach to the stability of external cavity modes in the Lang-Kobayashi system using the limit of large delay. SIAM J. Appl. Dyn. Syst. Volume 9, Issue 2, pp. 519-535 (2010).  PDF
15. P. Perlikowski, A. Stefanski, T. Kapitaniak: "Discontinuous synchrony in an array of Van der Pol oscillators", International Journal of Non-Linear Mechanics (2010), IJNLM, PDF
16. J. Grabski, J. Strzalko, A. Stefanski, P. Perlikowski and T. Kapitaniak: "Understanding coin tossing", The Mathematical Intelligencer (2010), Math. Intelligencer., PDF
17. S. Yanchuk and P. Perlikowski, Delay and periodicity, Phys. Rev. E. 79 (2009) 046221 (PDF).
18. B. Fiedler, S. Yanchuk, V. Flunkert, Ph. Hovel, H.-J. Wunsche, E. Schöll, Delay stabilization of rotating waves near fold bifurcation and application to all-optical control of a semiconductor laser, Phys. Rev. E 77 (2008) 066207. PDF
    
19. S. Yanchuk and M. Wolfrum, Destabilization patterns in chains of coupled oscillators, Phys. Rev. E 77 (2008) 026212. PDF
    
20. S. Yanchuk, K. Schneider. O. Lykova, Amplitude synchronization of two coupled lasers, Ukr. Math. J. 60 (Special issue dedicated to A.M. Samoilenko) (2008) pp. 426-435.
21. K. R. Schneider, S. Yanchuk, On a class of periodic boundary value problems appearing in lasers dynamics, Applicable Analysis 87 (2008), 723-731.
22. J. Grabski, J. Strzalko, A. Stefanski, P. Perlikowski and T. Kapitaniak: "The Dynamics of Coin Tossing is Predictable", Physics Reports, Volume 469, Issue 2, December 2008, Pages 59-92, (2008). PR, PDF
23. K. Czolczynski, A. Stefanski, P. Perlikowski T. Kapitaniak: "Multistability and chaotic beating of Duffing oscillators suspended on an elastic structure", Journal Sound and Vibration, accepted for publication, (2008). JSV.
24. P. Perlikowski, B. Jagiello, A. Stefanski, T. Kapitaniak: "Experimental observation of ragged synchronizability", Physical Review E, 78, 017203 (2008). PRE, PDF
25. P. Perlikowski, A. Stefanski, and T. Kapitaniak: "1:1 Mode locking and generalized synchronization in mechanical oscillators", Journal Sound and Vibration, doi:10.1016/j.jsv.2008.04.021, (2008). JSV, PDF
26. P. Perlikowski, A. Stefanski, and T. Kapitaniak: "Comment on Synchronization in a ring of four mutually coupled van der Pol oscillators: Theory and experiment"", Physical Review E, 77, doi:048201 (2008). PRE, PDF
27. P. Perlikowski: "Synchronization of mechanical oscillators excited kinematically", Journal of Theoretical and Applied Mechanics, 48 (1), (2008).
28. K. Czolczynski, P. Perlikowski, A. Stefanski and T. Kapitaniak: "Clustering and synchronization of n Huygens' clocks", Physica A, 388,5013-5023  (2009).
29. K. Czolczynski, P. Perlikowski, A. Stefanski and T. Kapitaniak: "Clustering and synchronization of n Huygens' clocks", Physica A, (2009), accepted

Book

J. Strzalko, J. Grabski, P. Perlikowski, A. Stefanski and T. Kapitaniak, "Dynamics of Gambling: Origins of Randomness in Mechanical Systems", Series: Lecture Notes in Physics , Vol. 792 , Springer, ISBN: 978-3-642-03959-1 (2010)

Chapters in books

1. P. Perlikowski, A. Stefanski, and T. Kapitaniak: "Ragged Synchronizability and Clustering in a Network of Coupled Oscillators", Recent Advances in Nonlinear Dynamics and Synchronization (NDS-1) - Theory and Applications, Springer, (2009).
2. J. Strzalko, J. Grabski, A. Stefanski, P. Perlikowski and T. Kapitaniak, "Dynamics of the coin tossing", Topics on Chaotic Systems, Selected Papers from CHAOS 2008 International Conference, World Scientific, (2009) World Scientific.
3. P. Perlikowski, A. Stefanski and T. Kapitaniak, "Ragged Synchronizability of Coupled van der Pols Oscillators", Nonlinear Dyanamics, Narosa Publishing House, New Delhi, India , (2009), Narosa Publishing House
4. L. Lücken and S. Yanchuk, Emergence of one- and two-cluster states in populations of globally pulse-coupled oscillators, in Nonlinear Laser Dynamics: From Quantum Dots to Cryptography, (Jonh Wiley, 2011), Ch. 12, pp. 293-316.

Organized meetings

• Minisymposium "Dynamics of Coupled Phase Oscillators" (Berlin, October 12, 2009)

• Ehrenkolloquium anlasslich des 70. Geburtstages von Klaus R. Schneider (Berlin, June 11, 2009)

• Workshop "Complex dynamics in large coupled systems" (Berlin, November 17-19, 2008)

• Symposium "Dynamics of Coupled Systems and Applications to Neurodynamics" (Berlin, July 1, 2008)

• Regular research seminar "Applied Analysis"
  

Links to some of our cooperation partners