This theorem can be applied to a great many complex dynamical networks in the real world.
Hence, the model investigated in this paper may characterize many natural dynamical networks and our proposed method can also be applied to more general dynamical networks.
Over the past decade, for better modeling and describing the large-scale physical systems consisting of interactive individuals, many kinds of dynamical networks coupled with continuous- or discrete-time dynamical systems have been introduced [1 26].
We consider climate as a network of many dynamical systems and apply ideas from graph theory to a global data set to study its collective behavior.
Some less restrictive structures found in some coupled dynamical networks also have many of the features of symmetric networks (including invariant subspaces, bifurcations that appear to be degenerate, and heteroclinic attractors) but without necessarily having the symmetries.
There are many interesting collective phenomena in complex dynamical networks that can be described by coupled differential equation equations, such as self-organization, synchronization, spatiotemporal chaos and so on.
Because the synchronization of complex dynamical networks can well explain many natural phenomena observed and is one of the important dynamical mechanisms for creating order in complex dynamical networks, the synchronization of coupled dynamical networks has come be a focal point in the study of nonlinear science.
Complex dynamical networks are being studied across many fields of science and engineering today.
We therefore observe many dynamical processes being studied on top of these networks, such as diffusion processes [30, 31], synchronization [32, 33], percolation [34, 35], etc.
During the last two decades, synchronization and control problems of complex dynamical networks have been focused on in many different fields such as mathematics, engineering, social and economic science, etc. [1 8].
