Finite-Time Bounded Synchronization of the Growing Complex Network with Nondelayed and Delayed Coupling

Abstract

The objective of this paper is to discuss finite-time bounded synchronization for a class of the growing complex network with nondelayed and delayed coupling. In order to realize finite-time synchronization of complex networks, a new finite-time stable theory is proposed; effective criteria are developed to realize synchronization of the growing complex dynamical network in finite time. Moreover, the error of two growing networks is bounded simultaneously in the process of finite-time synchronization. Finally, some numerical examples are provided to verify the theoretical results established in this paper.

Uniqueness and Novel Finite-Time Stability of Solutions for a Class of Nonlinear Fractional Delay Difference Systems

“…Proof. Let ( ) and̃( ) be any two different solutions to system (7), then ( ) and̃( ) both satisfy (13). Let ( ) = ( ) −̃( ).…”

“…One can extend the constant matrices in (7) to the function form as follows: Δ ] ( ) = ( ) ( ) + ( ) ( − ℎ ( )) + ( ) ( ) + ( , ( ) , ( − ℎ ( )) , ( )) ,…”

“…Suppose that ] = 1/20, and (⋅) = 0.1 sin ( ) + 0.1 cos ( − ℎ( )) with = ( 1 ( ), 2 ( )) . Consider system (7), where…”

“…There is a growing tendency nowadays that many experts show their great enthusiasm for fractional difference equations, and in the past few years, a lot of achievements have been done. For an extensive collection of such results, we recommend the readers to monograph [2] and papers [3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

“…In [19,22], the coefficients of the fractional discrete system researched by authors are one-dimensional real numbers which are too simple to describe the mathematical model well, and we adopt constant matrices as coefficients in (7). Therefore, the generalized models are originally discussed in the present paper.…”