TY - JOUR
T1 - Fastest synchronized network and synchrony on the Julia set of complex-valued coupled map lattices
AU - Liang, Yu Hao
AU - Wu, Wan Rou
AU - Jonq, Juang
PY - 2016/1/1
Y1 - 2016/1/1
N2 - The purpose of this paper is to address synchronous chaos on the Julia set of complex-valued coupled map lattices (CCMLs). Our main results contain the following. First, we solve an inf min max problem for which its solution gives the fastest synchronized rate in a certain class of coupling matrices. Specifically, we show that for the class of real circulant matrices of size 4, the coupling weights, possible complex numbers, yielding the fastest synchronized rate can be exactly obtained. Second, for individual map of the form fc(z) = z2 + c with /c/ < 1/4 , we show that the corresponding CCMLs acquires global synchrony on its Julia set with the number of the oscillators being 3 or 4 for the diffusive coupling. For c = 0 and -2, the corresponding CCMLs obtain local synchronization if and only if the number of oscillators is less than or equal to 5. Global synchronization for the individual map of the form gc(z) = z3 + cz is also reported.
AB - The purpose of this paper is to address synchronous chaos on the Julia set of complex-valued coupled map lattices (CCMLs). Our main results contain the following. First, we solve an inf min max problem for which its solution gives the fastest synchronized rate in a certain class of coupling matrices. Specifically, we show that for the class of real circulant matrices of size 4, the coupling weights, possible complex numbers, yielding the fastest synchronized rate can be exactly obtained. Second, for individual map of the form fc(z) = z2 + c with /c/ < 1/4 , we show that the corresponding CCMLs acquires global synchrony on its Julia set with the number of the oscillators being 3 or 4 for the diffusive coupling. For c = 0 and -2, the corresponding CCMLs obtain local synchronization if and only if the number of oscillators is less than or equal to 5. Global synchronization for the individual map of the form gc(z) = z3 + cz is also reported.
KW - Complex-valued coupled map lattices
KW - Fastest synchronized network
KW - Julia set
UR - http://www.scopus.com/inward/record.url?scp=84948683059&partnerID=8YFLogxK
U2 - 10.3934/dcdsb.2016.21.173
DO - 10.3934/dcdsb.2016.21.173
M3 - Article
AN - SCOPUS:84948683059
VL - 21
SP - 173
EP - 184
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
SN - 1531-3492
IS - 1
ER -