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Section DYNAMICS IN LIFE SCIENCES, NEUROSCIENCE APPLICATIONS WORKSHOP
However, unlike the model discussed in [7], our model provides an explicit analytical description of the linear response function in (3) and, therefore, allows performing analytical stability analysis of the CW solutions. Apart from FDML lasers the approach discussed here can be applied to study the dynamics of mode-locked photonic crystal [7] and other types of multimode lasers.
Acknowledgements
We gratefully acknowledge useful discussions with Julien Javaloyes, Svetlana Gurevich, Svetlana Slepneva, and Shal-va Amiranashvili. A.G.V. and A.P. acknowledge the support of SFB 787 of the DFG. A.G.V. acknowledges the support of the grant 14-41-00044 of Russian Scientific Foundation.
References
1. H. A. Haus, IEEE J. Sel. Top. Quantum Electron., 2000, 6(6), 1173-1185.
2. U. Bandelow, M. Radziunas, J. Sieber, and M. Wolfrum, IEEE J. Quantum Electron., 2001, 37, 183-188.
3. A. G. Vladimirov and D. Turaev, Phys. Rev. A, 2005, 72, 033808.
4. S. Slepneva, B. Kelleher, B. O'Shaughnessy, S. Hegarty, A. G. Vladimirov, and G. Huyet, Opt. Express, 2013, 21(16), 19240-19251.
5. S. Slepneva, B. O'Shaughnessy, B. Kelleher, S. Hegarty, A. G. Vladimirov, H. Lyu, K. Karnowski, M. Wojtkowski, and G. Huyet, Opt. Express, 2014, 22(15), 18177-18185.
6. S. Yanchuk and M. Wolfrum, SIAM J. Appl. Dyn. Syst., 2010, 9, 519-535.
7. M. Heuck, S. Blaaberg, and J. Mark, Opt. Express, 2010, 18(17), 18003-18014.
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Optimal Extraction of Collective Rhythmicity from Unreliable EEG Channels
Justus Schwabedal*
Max-Planck-Institute for the Physics of Complex Systems,Germany. * Presenting e-mail: jschwabedal@gmail.com
I present a novel data-processing method that facilitates the detection and analysis of the irregular-oscillatory dynamics. The method is particularly useful to EEG analysis, as I will demonstrate in polysomnographic EEG recordings. By design, the method copes well with unreliable recordings showing fluctuating signal amplitude, phase offsets, and substantial amounts of measurement noise. Under such relatively general conditions, I will show that the method optimally enhances a rhythm of interest, and demonstrate its use by the detection and analysis of EEG sleep spindles.
Active Wireless Networks for Experimental Study in Neuroscience
AS. Dmitriev*, R.Y. Emelyanov, M.Yu. Gerasimov
Institute of Radio Engineering and Electronics. VA Kotelnikov RAS, Moscow Institute of Physics and Technology * Presenting e-mail: chaos@cplire.ru
The report examines the active wireless network, which can serve as an experimental tool in the study of various objects in neurodynamics. The network combines the nodes on which digital or analog neuron model (if necessary this may be living neurons), and programmable connections between them, which are implemented through wireless channels can be implemented. The latter circumstance allows the implementation of any type of connection (Linear. Non-linear, with delay, etc.) with any desired topology As an example, the modeling of the phenomenon of chimeras in the system of coupled oscillators is presented.
Chimeras - a popular and interesting phenomenon in the oscillator system [1], which are mainly studying by computer simulation. Experimental study of chimeras, in particular, in small ensembles requires special experimental setups. The active wireless network [2] is used as such experimental equipment in the report. Experiments were carried out with small ensemble of coupled oscillators. Ensemble of six phase oscillators [3] was using as the study system:
Section DYNAMICS IN LIFE SCIENCES, NEUROSCIENCE APPLICATIONS WORKSHOP
where g(q>) = - sin(q> - a) + r sin(2q>) is coupling strength function, i = 1, . . . , 3, j = 0, 1.
Thus, the ensemble consists of two groups of three oscillators, the oscillators within the group connected with coupling coefficient equal 1 and oscillators of the various groups - with coupling coefficient £. This ensemble demonstrates chimeric state in which one part of the oscillators is synchronized in frequency, and the other part of the oscillators - no. Each active node in the wireless network is implemented as a pair of ultra-wideband wireless transceiver and the connected actuator. The actuator is a card equipped with a microcontroller, as a calculating device, and multicolor LEDs as a visualization tool. To simulate an ensemble of coupled oscillators, each oscillator in the experiments of the ensemble is associated with a node is an active network. The equation of the oscillator are integrated on the microcontroller, the communication between the oscillators are realized through wireless channels, and the oscillator phase is visualized by means of colored LEDs. This approach allows an arbitrary network topology and a visual demonstration of dynamic patterns of the ensemble.
The report examines the technique of modeling with the help of the active wireless network, the experimental results of the observation of different dynamic regimes of the ensemble and their analysis. The study was performed by a grant from the Russian Science Foundation (Project № 16-19-00084)
References
1. Kuramoto Y. Chemical oscillations, waves and turbulence. Berlin : Springer-Verlag. 1984.
2. Dmitriev A. S., Yemelyanov R. Yu., Gerasimov M. Yu., Itskov V. V. Active ultra wideband wireless networks usage for modelling ensembles of nonlinear continuous time dynamical systems //Nonlinear phenomena in complex systems. 2015. V. 18. №. 4. P. 456-466.
3. Ashwin P., Burylko O. Weak chimeras in minimal networks of coupled phase oscillators //Chaos: An Interdisciplinary Journal of Nonlinear Science. 2015. V. 25. №. 1. P. 013106.
On the Dynamics of Some Small Hypercycles with Short-Circuits
Josep Sardanyés1, J. Tomás Lazaro2*, Toni Guillamon3, and Ernest Fontich4
1 ICREA-Complex Systems Lab, Universitat Pompeu Fabra and Institut de Biología Evolutiva CSIC-UPF, Barcelona, Spain;
2 Departament de Matemàtiques Universitat Politécnica de Catalunya and Barcelona Graduate School of Mathematics BGSMath, Barcelona, Spain;
3 Departament de Matemàtiques Universitat Politécnica de Catalunya and Barcelona Graduate School of Mathematics BGSMath, Barcelona, Spain;
4 Departament de Matemàtiques i Informática Universitat de Barcelona and Barcelona Graduate School of Mathematics BGSMath, Barcelona, Spain.
* Presenting e-mail: jose.tomas.lazaro@upc.edu
It is known that hypercycles are sensitive to the so-called parasites and short-circuits. While the impact of parasites has been widely investigated for well-mixed and spatial hypercycles, the effect of short-circuits in hypercycles remains poorly understood. In this talk we will present, briefly, a description of the mean field and spatial dynamics of two small, asymmetric hypercycles with short-circuits: first, we consider a 2-member hypercycle with one of the species containing an autocatalytic loop, which represents the simplest case with a short-circuit; second, we add a third species which closes the 3-member hypercycle and preserving the initial autocatalytic short-circuit and the 2-member inner cycle. We characterize the bifurcations and transitions involved in the dominance of the short-circuits and in hypercycles' size. The spatial simulations reveal a random-like and mixed distribution of the hypercycle species in the all-species coexistence scenario, ruling out the presence of large-scale spatial patterns such as spirals or spots typical of larger hypercycles. MonteCarlo simulations reveal a drastic decrease of the probability of finding stable hypercycles with short-circuits when passing from the 2-member to the 3-member scenario.
Acknowledgements
We want to thank Ricard Solé and José Antonio Darós for their comments and fruitful discussions. This work has been partially funded by the Botín Foundation, by Banco Santander through its Santander Universities Global Division (JS); the Spanish grants MINECO MTM2013-41168-P (EF), MTM2015-71509-C2-2-R (TG) and MTM2015-65715-P (JTL); the Catalan grants AGAUR 2014SGR-1145 (EF) and 2014SGR-504 (TG, JTL); the grant 14-41-00044 of RSF at the Lobachevsky University of Nizhny Novgorod (Russia) (JTL); and the European Marie Curie Action FP7-PEOPLE-2012-IRSES: BREUDS (JTL).
OM&P
