Control of Self-Organizing Nonlinear Systems by Eckehard Schöll, Sabine H. L. Klapp, Philipp Hövel
By Eckehard Schöll, Sabine H. L. Klapp, Philipp Hövel
The e-book summarizes the cutting-edge of study on regulate of self-organizing nonlinear structures with contributions from top foreign specialists within the box. the 1st concentration issues fresh methodological advancements together with keep watch over of networks and of noisy and time-delayed platforms. As a moment concentration, the publication positive aspects rising thoughts of program together with keep watch over of quantum structures, smooth condensed topic, and organic platforms. exact issues reflecting the lively study within the box are the research and keep an eye on of chimera states in classical networks and in quantum platforms, the mathematical therapy of multiscale structures, the keep watch over of colloidal and quantum shipping, the regulate of epidemics and of neural community dynamics.
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The average has been performed over a time window TW = 200, after discarding a transient time TR = 5,000−50,000 depending on the system size; the larger TR have been employed for the larger N 38 S. Olmi and A. Torcini By observing all the data reported in Fig. 8, while the transition to PS is clearly subcritical. These results confirm the analysis reported in  for a system with noise (in particular, see Fig. 17 in that paper). However, Acebrón et al. affirm that the SW is stable, while the TW is unstable.
The data reported so far refer to a single system size, however finite size effects are quite relevant for this model, as shown in  for unimodal distributions. In Fig. 7a we report the synchronization transition for several system sizes, namely 1,000 ≤ N ≤ 50,000 for a small inertia value (m = 1). We observe that K T W and K SW increase with the size N ; in particular, the incoherent state is observable on a wider coupling interval by increasing N (similarly to what reported in  for unimodal distributions).
Tinsley, K. Showalter, Chimera states in populations of nonlocally coupled chemical oscillators. Phys. Rev. Lett. 110, 244102 (2013) 19. J. Hizanidis, V. Kanas, A. Bezerianos, T. Bountis, Chimera states in networks of nonlocally coupled hindmarsh-rose neuron models. Int. J. Bifurcat. Chaos 24(03), 1450030 (2014) 20. C. Sethia, A. L. Johnston, Amplitude-mediated chimera states. Phys. Rev. E 88(4), 042917 (2013) 21. C. Sethia, A. Sen, Chimera states: the existence criteria revisited. Phys. Rev. Lett.