Finite-time stochastic outer synchronization between two complex dynamical networks with different topologies

In this paper, we investigate the lag outer synchronization problem of complex dynamical networks with noise coupling. Based on the stability theory of stochastic differential equations, we obtain the sufficient conditions for the lag outer synchronization. The theoretical results show that the lag outer synchronization could be achieved only via white noise-based coupling. Furthermore, we show that noise can also be used to enhance the lag outer synchronization between two networks when two networks have both conventional linear coupling and white noise-based coupling. Finally, numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

The theory of stochasic integrals and stochastic differential equations was established by K Ito [3, 4] (also see [2]). In past four decade years, Ito’s stochastic analysis has established for itself the central role in modern probability theory. Ito’s theory of stochastic differential equations has been one of the most important tools. However, Ito’s construction of stochastic integrals over Brownian motion possesses an essentially random characterization, and is meaningless for a single Brownian path. The Ito map obtained by solving Ito’s stochastic differential equations is nowhere continuous on the Wiener space.

Robust synchronization in finite time for fractional-order hybrid coupling discontinuous complex dynamic networks with nonlinear growth

This paper uses stochastic differential equation and risk theory to study the probability model of insurance company's bankruptcy function and the proportion model of financial insurance investment. It also studies the application of stochastic probability to the investment decision-making of institutional investors. Taking the four major insurance industries in China as an example, it gives the strategy of venture capital.

Finite-time synchronization of complex dynamical networks under delayed impulsive effects

A theory of stochastic differential equations driven by predictable processes in Stratonovich sense is developed. These driving processes include a large class of discontinuous semimartingales. The theory of stochastic differential equations driven by continuous semimartingales in Stratonovich sense is extended without involving Lebesgue-Stieltjes integrals as done by Meyer. Moreover, a change of variables formula without extra terms involving the jumps of the processes holds for this theory. Results on approximation of driving processes are preserved.

The paper investigates the problem of finite-time projective synchronization between two different complex networks, where two complex networks may be different in the node dynamics, or in the topological structures. By using a finite-time stability theorem and inequality techniques, a sufficient criterion is derived based on Lyapunov stability theory, in the form of linear matrix inequalities (LMIs). The LMIs are readily solved by the LMI toolbox in Matlab. At last, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method. It is worth noting that the coupling configuration matrix is not necessarily symmetric or irreducible; and the inner coupling matrix does not need to be symmetric.

Complex networks are everywhere.Synchronization is a very important nonlinear phenomenon which universally exists in nature.Over the last decade,many researchers have further investigated the synchronization of complex dynamical networks,including identical synchronzation,clustering synchronization,partial synchronization,and so on.The characterization of synchronous speed of complex dynamical networks in most known res(?)lts is asymptotic.That is,complex networks can realize synchronization only when the time t tends to infinity.However,there are few results reported on how long complex networks can reach synchronization.Based on two kinds of typical complex dynamical networks with nonlinear coupling,this paper will further explore the finite-time synchronization of complex dynamical networks.In detail,under some suitable conditions,it is proved that the above complex dynamical networks can realize accurate synchronization within finite- time.Moreover,a typical numerical simulation is then given to validate the effectiveness of the proposed criteria for finitetime synchronization.It should be especially pointed out that the finite-time synchronization sucessfully overcomes the difficulty of infinite synchronous time.The above results have some important practical meaning for the real-world engineering application.

In this paper, we address the problem of finite-time adaptive synchronization of two-layer networks, and take the effect of stochastic perturbation into consideration. By adopting the integrated control protocols including a finite-time controller and an adaptive controller, sufficient conditions for realizing synchronization of two-layer networks with identical and nonidentical topologies are derived based on the finite-time stability theory of (stochastic) differential equations. Besides, a wide range of finite-time adaptive synchronization in multilayer networks can be achieved under the proposed strategies. Finally, the classical Chen system and Lorenz system are taken as the examples of node dynamics to illustrate the effectiveness and feasibility of the theoretical results.

Finite-time synchronization of drive-response systems via periodically intermittent adaptive control

In this paper, mixed outer synchronization between two different complex dynamical networks without and with time-varying delayed couplings is investigated. By pinning only a fraction of the nodes in the response network, some effective mixed outer synchronization criteria are obtained based on the Lyapunov stability theory. As a result, the mixed outer synchronization between two complex networks is achieved. Then, in the view of the generalized time-varying delayed different inequalities, some sufficient conditions for mixed outer exponential synchronization are derived by imposing the impulsive controllers to the nodes of the corresponding response network. Finally, some numerical simulations are presented to demonstrate the effectiveness and feasibility of the results we obtained in this paper.

Global synchronization of coupled map lattices are investigated in this paper. A sufficient condition for global synchronization is derived. Unlike other approaches, the coupled lattices is not linearized in this paper. Instead, the sufficient condition for the synchronization is obtained here by introducing a reference state along with Lyapunov function method, and this condition is simply given in terms of the maximum absolute value of eigenvalues of the coupling matrices those are not equal to one. Moreover, we give how to construct the coupling matrix to guarantee global synchronization of coupled map lattices based on two comparing matrices, which is very convenient to use. A typical example of coupled map lattices with chaotic nodes is finally used to verify the theoretical results and the effectiveness of the proposed synchronization scheme.

Exploring synchronizability of complex dynamical networks from edges perspective

In this paper, we investigate lag synchronization problem of complex dynamical network with noise coupling. Based on the theory of stochastic differential equations, we obtain the sufficient conditions about lag synchronization of complex network with noise coupling. The theoretical results show that lag synchronization could be achieved via white-noise-based coupling. Finally, numerical simulations are presented to demonstrate the effectiveness of proposed schemes.

Global mean square exponential stability of stochastic neural networks with retarded and advanced argument