Finite-Time Function Projective Synchronization in Complex Multi-links Networks with Time-Varying Delay

Finite-time mixed outer synchronization of complex networks with time-varying delay and unknown parameters

The global finite-time synchronization control of a type of fourth-order hyperchaotic systems with intersecting nonlinearities was studied. Firstly, the matrix form of this kind of hyperchaotic system was given to construct the master-slave synchronization models based on the generalized linear state error feedback controller. Then, the finite-time synchronization problem was equivalent to the finite-time stability of the error system originating from the master-slave hyperchaotic systems. The global finite-time stability of the error system was proven by the finite-time stability theory, further obtaining the criterion for global finite-time synchronization and the synchronization time estimation in mathematical formula. Subsequently, the theoretical results were applied to the well-known hyperchaotic Lorenz-stenflo system. The finite-time synchronization criteria for hyperchaotic Lorenz-stenflo systems were further proven by using optimization technology, and the corresponding synchronization times were estimated. Finally, the simulation was conducted by the MATLAB software, showing that two hyperchaotic Lorenz-stenflo systems could synchronize in a finite time.

The finite-time synchronization of coupled inertial memristive neural networks (IMNNs) systems is discussed in this paper. Firstly, a mathematical model of IMNNs with time-varying delays is given, then the original system is transformed into a first-order differential equation by selecting a suitable variable substitution. Secondly, by using two different controllers and the definition of the upper right-hand derivative, it can be guaranteed that finite-time and fixed-time synchronization between response system and drive system based on finite time stability and fixed time theory. Finally, two numerical simulations are given to illustrate the effectiveness of the main results.

Function projective synchronization in complex dynamical networks with time delay via hybrid feedback control

The finite-time passivity problem is, respectively, investigated for stochastic coupled complex networks (SCCNs) with and without time-varying delay. Firstly, we present several new concepts about finite-time passivity in the sense of expectation on the basis of existing passivity definition. By designing appropriate controllers, the finite-time passivity of SCCNs with and without time-varying delay is obtained. In addition, the definition of finite-time synchronization in the sense of expectation is proposed. Under some sufficient conditions and designed controllers, finite-time passivity derives finite-time synchronization. Finally, two examples are given to demonstrate the effectiveness of finite-time passive and synchronization criteria.

Finite-time synchronization of memristive neural networks with discontinuous activation functions and mixed time-varying delays

Finite-time synchronization of inertial memristive neural networks with time delay via delay-dependent control

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 multi-layer nonlinear coupled complex networks via intermittent feedback control

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

In this paper, we consider a general and practical complex network model, in which there exist couplings with and without time delays, and the coupled functions among nodes are also nonlinear. For this network model, we investigate its finite-time synchronization by designing some general static and adaptive controllers respectively. Using the finite-time stability theory, some useful finite-time synchronization criteria are derived. Finally, numerical simulations are given to demonstrate the correctness of our theoretical results.

Although function projective synchronization in complex dynamical networks has been extensively studied in the literature, few papers deal with the problem between two different complex networks with correlated random disturbances. In this paper, we present some novel techniques to analyze the problem of synchronization. A probability approach is introduced to obtain an almost sure synchronization criterion. We also present some efficient approaches to analyze the problem of exponential synchronization. For the problem of synchronization in some complex networks, our approaches not only can replace the LaSalle-type theorem but also allow improvements of existing results in the literature. Finally, some numerical examples are provided to demonstrate the effectiveness of the proposed approaches.

Non-separation method-based robust finite-time synchronization of uncertain fractional-order quaternion-valued neural networks

In this paper, finite-time synchronization (FTS) problems in an array of unified chaotic and hyperchaotic systems are mainly studied using some important control methods. First, FTS and finite-time transmission synchronization (FTTS) for N systems are realized in a finite time by designing the effective control schemes, and the stability criteria can be given. The corresponding examples are presented to show the effectiveness and feasibility of the controllers proposed by considering three chaotic and hyperchaotic systems.

Finite-time and fixed-time bipartite synchronization of complex networks with signed graphs