By Eckehard Schöll, Sabine H. L. Klapp, Philipp Hövel
The e-book summarizes the state of the art of study on regulate of self-organizing nonlinear structures with contributions from top overseas specialists within the box. the 1st concentration matters fresh methodological advancements together with regulate of networks and of noisy and time-delayed structures. As a moment concentration, the e-book positive factors rising strategies of software together with keep watch over of quantum structures, gentle condensed subject, and organic structures. specific issues reflecting the lively learn within the box are the research and keep watch over of chimera states in classical networks and in quantum structures, the mathematical remedy of multiscale structures, the regulate of colloidal and quantum delivery, the regulate of epidemics and of neural community dynamics.
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Extra resources for Control of Self-Organizing Nonlinear Systems
Sample text
This state is characterized by a cluster of N L locked; if now we reduce the coupling K , the number of locked oscillators remain constant until we do not reach the descending curve obtained with protocol (II), see the black empty triangles in Fig. 2. On the other hand r¯ decreases slightly with K , this behavior is well reproduced by the mean field I solutions of Eq. 9), namely r 0 (K , Ω0 ) with Ω0 = Ω P (K s , r I (K S )) = π4 Kms r , these are shown in Fig. 2a as black dot-dashed lines. As soon as, by decreasing 2 Dynamics of Fully Coupled Rotators … 33 K , the frequency Ω0 becomes equal or smaller than Ω D , the order parameter has a rapid drop towards zero following the upper limit curve r I I .
Panels (b) and (d) display the order parameter r (t) (black line) versus time for the same coupling constants as in (a) and (c), respectively. The dashed black (continuous grey) line denotes the time evolution of r p (rn ). For each simulation an initial transient time TR = 1000 has been discarded and the average are estimated over a time interval TW = 200. In both cases m = 2, N = 2000 and Ω0 = 2 2 Dynamics of Fully Coupled Rotators … 37 can be non perfectly symmetric. The asymmetric cluster will emerge around +Ω0 (−Ω0 ) depending on the positive (negative) sign of the average natural frequency.
Therefore, by appropriately choosing the value of time delay one can realize a desired lifetime of amplitude chimeras. 7 Conclusions We have investigated two types of chimera states for a paradigmatic network of oscillators under the influence of noise and time delay. We have presented numerical results demonstrating that transient amplitude chimeras and chimera death states in a ring network of identical Stuart-Landau oscillators with symmetry-breaking 1 Controlling Chimera Patterns in Networks: Interplay of Structure, Noise, and Delay 21 coupling continue to exist in the presence of Gaussian white noise or if time delay is introduced to the coupling.