Synchronization in Networks of Nonlinear Circuits by Mattia Frasca Lucia Valentina Gambuzza Arturo Buscarino & Luigi Fortuna

Author:Mattia Frasca, Lucia Valentina Gambuzza, Arturo Buscarino & Luigi Fortuna
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(3.20)

and obeying to:

(3.21)

where and , so that the reference trajectory is generated by a FHN system with slightly different parameters. In the case of IDC, we have considered Eq. (3.19) with .

Figure 3.4 shows the results for pinned nodes (the period of activation of the control is ). Figure 3.4 clearly shows how, after switching off the control, a chimera state appears with the coherent (incoherent) domain located in the region of pinned nodes, . The initial conditions for both panel in Fig. 3.4 are the same. We observe that in the case of IDC the external noise significantly influences the system behavior. This result is different from [14] where chimera states are shown to be robust to the presence of noise as the noise intensity is several orders of magnitude larger.

The MATLAB code to control chimera states in the ring of nonlocally coupled FHN units is reported in the following. Both strategies are implemented and may be selected commenting/uncommenting a few lines of the code. The simulation in the code starts from random initial conditions.

Fig. 3.4Local order parameter as in Eq. (3.16) with , for a ring of nonlocally coupled FHN. The system starts from the same initial condition of the simulation in Fig. 3.3. a Results of CDC with , , and ; b Results of IDC with . In both the cases, we have fixed and . The other parameters are , , , , , and

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