TY - JOUR
T1 - Generic behavior of master-stability functions in coupled nonlinear dynamical systems
AU - Huang, Liang
AU - Chen, Qingfei
AU - Lai, Ying-Cheng
AU - Pecora, Louis M.
PY - 2009/9/15
Y1 - 2009/9/15
N2 - Master-stability functions (MSFs) are fundamental to the study of synchronization in complex dynamical systems. For example, for a coupled oscillator network, a necessary condition for synchronization to occur is that the MSF at the corresponding normalized coupling parameters be negative. To understand the typical behaviors of the MSF for various chaotic oscillators is key to predicting the collective dynamics of a network of these oscillators. We address this issue by examining, systematically, MSFs for known chaotic oscillators. Our computations and analysis indicate that it is generic for MSFs being negative in a finite interval of a normalized coupling parameter. A general scheme is proposed to classify the typical behaviors of MSFs into four categories. These results are verified by direct simulations of synchronous dynamics on networks of actual coupled oscillators.
AB - Master-stability functions (MSFs) are fundamental to the study of synchronization in complex dynamical systems. For example, for a coupled oscillator network, a necessary condition for synchronization to occur is that the MSF at the corresponding normalized coupling parameters be negative. To understand the typical behaviors of the MSF for various chaotic oscillators is key to predicting the collective dynamics of a network of these oscillators. We address this issue by examining, systematically, MSFs for known chaotic oscillators. Our computations and analysis indicate that it is generic for MSFs being negative in a finite interval of a normalized coupling parameter. A general scheme is proposed to classify the typical behaviors of MSFs into four categories. These results are verified by direct simulations of synchronous dynamics on networks of actual coupled oscillators.
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U2 - 10.1103/PhysRevE.80.036204
DO - 10.1103/PhysRevE.80.036204
M3 - Article
C2 - 19905197
AN - SCOPUS:70349770732
SN - 1539-3755
VL - 80
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 3
M1 - 036204
ER -