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

Y1 - 2016/1

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

SN - 1531-3492

VL - 21

SP - 173

EP - 184

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 1

ER -