A new class of controlled time-varying complex dynamical networks with similarity is investigated and a decentralized holographic-structure controller is designed to stabilize the network asymptotically at its equilibrium states. The control design is based on the similarity assumption for isolated node dynamics and the topological structure of the overall network. Network synchronization problems, both locally and globally, are considered on the ground of decentralized control approach. Each sub-controller...

In this paper, we study differential equations arising from the generating functions of the generalized Bell polynomials.We give explicit identities for the generalized Bell polynomials. Finally, we investigate the zeros of the generalized Bell polynomials by using numerical simulations.

We prove a convergence result for a time discrete process of the form $x(t+h)-x\left(t\right)=hV(h,x(t+{\alpha }_1\left(t\right)h),...,x(t+{\alpha }_L\left(t\right)h))t=T+jh,j=0,...,\sigma \left(h\right)-1$ under weak conditions on the function $V$. This result is a slight generalization of the convergence result given in [5].Furthermore, we discuss applications to minimizing problems, boundary value problems and systems of nonlinear equations.