8.4 Synchronization Phenomena in the NMCC
337
Fig. 8.8 Zoom of the waveforms in Fig. 8.7 over time intervals [0, 25] (upper part) and [60, 100]
(bottom part)
8.4.1.2 Periodic and Chaotic Clusters in NMCC
Suppose to keep ICs values as in the previous case (i.e., ϕ 0 = 0, ¯
ϕ 0,1 = 1.1, and
¯
ϕ 0,2 = ¯
ϕ 0,3 = ¯
ϕ 0,4 = −1), but α = 8 changes over to α = 9.5, thus each uncoupled
MCC exhibits on the zero-manifold M(0) a double-scroll chaotic attractor (see
Fig. 8.3 in Sect. 8.2.1). In such a case the change of parameter α induces a (standard)
bifurcation and the complex dynamic scenario is reported in Figs. 8.10 and 8.11
for d = 0.005 and Fig. 8.12 for d = 0.05. From Fig. 8.11 it is seen that when
d = 0.05 the whole NMCC exhibits a chaotic attractor such that the external 1st
and 4th MCCs have a periodic synchronized behavior whereas the internal 2nd and
337
Fig. 8.8 Zoom of the waveforms in Fig. 8.7 over time intervals [0, 25] (upper part) and [60, 100]
(bottom part)
8.4.1.2 Periodic and Chaotic Clusters in NMCC
Suppose to keep ICs values as in the previous case (i.e., ϕ 0 = 0, ¯
ϕ 0,1 = 1.1, and
¯
ϕ 0,2 = ¯
ϕ 0,3 = ¯
ϕ 0,4 = −1), but α = 8 changes over to α = 9.5, thus each uncoupled
MCC exhibits on the zero-manifold M(0) a double-scroll chaotic attractor (see
Fig. 8.3 in Sect. 8.2.1). In such a case the change of parameter α induces a (standard)
bifurcation and the complex dynamic scenario is reported in Figs. 8.10 and 8.11
for d = 0.005 and Fig. 8.12 for d = 0.05. From Fig. 8.11 it is seen that when
d = 0.05 the whole NMCC exhibits a chaotic attractor such that the external 1st
and 4th MCCs have a periodic synchronized behavior whereas the internal 2nd and