The Curvature Index and Synchronization of Dynamical Systems


Yen-Sheng Chen

13:00:00 - 15:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

For a dynamical system, it is important to characterize a property of the system by a quantity. These quantities convey different physical meanings, and they are useful in the fields of dynamical system and other practical applications. We develop a quantity, named the curvature index, for dynamical systems. This index is defined as the limit of the average curvature of the trajectory during evolution, which measures the bending of the curve on an attractor. The curvature index has the ability to differentiate the topological change of an attractor, as its alterations exhibit the structural changes of a dynamical system. Thus, the curvature index may indicate thresholds of some synchronization regimes. The Rossler system and a time-delay system are simulated to demonstrate the effectiveness of the index, respectively.