TY - JOUR
T1 - Chaos in the fractional order unified system and its synchronization
AU - Wu, Xiangjun
AU - Li, Jie
AU - Chen, Guanrong
PY - 2008/7
Y1 - 2008/7
N2 - The chaotic behaviors in the fractional order unified system are numerically investigated. By utilizing the fractional calculus techniques, we found that chaos exists in the fractional order unified system with order less than 3. The lowest order we found to have chaos in this system is 2.76. Chaos synchronization of the fractional order unified system is theoretically and numerically studied using the one-way coupling method. The suitable conditions for achieving synchronization of the fractional order differential system are derived by using the Laplace transform theory. It is noticed that the time required for achieving synchronization of the drive system and the response system and the synchronization effect sensitively depend on the coupling strength. Numerical simulations are performed to verify the theoretical analysis. © 2007 The Franklin Institute.
AB - The chaotic behaviors in the fractional order unified system are numerically investigated. By utilizing the fractional calculus techniques, we found that chaos exists in the fractional order unified system with order less than 3. The lowest order we found to have chaos in this system is 2.76. Chaos synchronization of the fractional order unified system is theoretically and numerically studied using the one-way coupling method. The suitable conditions for achieving synchronization of the fractional order differential system are derived by using the Laplace transform theory. It is noticed that the time required for achieving synchronization of the drive system and the response system and the synchronization effect sensitively depend on the coupling strength. Numerical simulations are performed to verify the theoretical analysis. © 2007 The Franklin Institute.
KW - Chaos synchronization
KW - Fractional order
KW - The Laplace transform theory
KW - The one-way coupling method
KW - The unified system
UR - http://www.scopus.com/inward/record.url?scp=41849090145&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-41849090145&origin=recordpage
U2 - 10.1016/j.jfranklin.2007.11.003
DO - 10.1016/j.jfranklin.2007.11.003
M3 - RGC 21 - Publication in refereed journal
SN - 0016-0032
VL - 345
SP - 392
EP - 401
JO - Journal of the Franklin Institute
JF - Journal of the Franklin Institute
IS - 4
ER -