Finite-time Lag Synchronization Research Articles

Finite-time lag synchronization for two-layer complex networks with impulsive effects

<abstract><p>This paper mainly considered the finite-time lag synchronization for two-layer complex networks with impulsive effects. Different types of controllers were designed to achieve the lag synchronization of two-layer complex networks. Several sufficient conditions on lag synchronization in the sense of finite time were derived. The time for synchronization was also estimated. It is important to note that synchronization time was influenced by the initial value, as well as the impulses and impulse sequence. This implied that different impulse effects result in varying synchronization times. Additionally, desynchronizing impulses can extend the synchronization time, whereas synchronizing impulses have the opposite effect. Finally, a numerical example was presented to showcase the practicality and validity of the proposed theoretical criteria.</p></abstract>

Finite-time lag synchronization for uncertain complex networks involving impulsive disturbances

This paper focuses on the finite-time lag synchronization (FTLS) of uncertain complex networks involving impulsive disturbance effects. By designing two different controllers, some Lyapunov-based conditions are established in terms of linear matrix inequalities to ensure the FTLS of impulsive systems, where the upper bound of the synchronizing times can be estimated via constructing Lyapunov functions. It is interesting to discover that the synchronizing time depends not only on the initial value but also on the impulse sequences, which implies that different impulses will lead to different synchronization times. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed FTLS criterion.

Finite-time lag synchronization of inertial neural networks with mixed infinite time-varying delays and state-dependent switching

In this article, we design a new control scheme to investigate the finite-time lag synchronization (FTLS) of inertial neural networks (INNs) with mixed infinite time-varying delays and state-dependent switching. Several novel and easily verified conditions are gained guaranteeing the FTLS of INNs via the finite-time stability theory and nonsmooth analysis. Moreover, it is worth emphasizing that here we directly analyze INNs without using variable substitution, which is different from the reduced-order approach used in correspondingly previous works. At last, a numerical example and an application in image encryption are given to verify the correctness and practicability of the obtained results.

Finite-Time Projective Lag Synchronization and Identification between Multiple Weights Markovian Jumping Complex Networks with Stochastic Perturbations

Two nonidentical dimension Markovian jumping complex networks with stochastic perturbations are taken as objects. The network models under two conditions including single weight and double weights are established, respectively, to study the problem of synchronization and identification. A finite-time projection lag synchronization method is proposed and the unknown parameters of the network are identified. First of all, based on Itô’s formula and the stability theory of finite-time, a credible finite-time adaptive controller is presented to guarantee the synchronization of two nonidentical dimension Markovian jumping complex networks with stochastic perturbations under both conditions. Meanwhile, in order to identify the uncertain parameters of the network with stochastic perturbations accurately, some corresponding sufficient conditions are given. Finally, numerical simulations under two working conditions are given to demonstrate the effectiveness and feasibility of the main theory result.

Finite-Time Lag Synchronization of Memristive Neural Networks With Multi-Links via Adaptive Control

The finite-time lag synchronization problem of memristive neural networks with multi-links (MNNLs) is discussed with the adaptive controllers, and the discrete and distributed time-varying delays are included in the network models. With the Lyapunov functional method and the properties of inequality, two different finite-time methods are adopted to prove and compare the effects of the two proposed theorems, and three corollaries are obtained and to be analyzed. Using the assumptions of Lipschitz continuous and boundedness of the activation functions, three lemmas are derived to deal with the difficulty caused by the memristive jumping properties and synchronization lag feature, which make the proof of the theorems simple and clear. Based on that whether time-varying delays are included, with the adaptive control strategy, we design delay-independent and delay-dependent adaptive controllers with different adaptive parameters for the MNNLs respectively. Finally, two numerical simulations are given to show the effectiveness and correctness of the obtained theoretical results.

Finite-Time Lag Synchronization of Uncertain Complex Dynamical Networks With Disturbances via Sliding Mode Control

This paper investigates lag synchronization between two uncertain complex dynamical network with time-varying coupling delay, fully unknown parameters, and disturbances in finite-time. First, a nonsingular terminal sliding surface is proposed and its finite convergence is proved. Then, appropriate adaptive laws are derived to estimate the unknown parameters of the networks. Subsequently, based on the finite-time stability theory and adaptive laws, an adaptive sliding mode control is designed for achieving finite-time lag synchronization. In addition, the unknown bounded disturbances are also overcame by the proposed control and some corollaries are given. Finally, analytical results show that the states trajectory of the networks error converge to the sliding phase within finite-time. Furthermore, numerical simulation results demonstrate the applicability and the effectiveness of the designed method.

Finite-time lag synchronization of coupled reaction–diffusion systems with time-varying delay via periodically intermittent control

ABSTRACTIn this paper, the issue of finite-time lag synchronization of coupled reaction–diffusion systems with time-varying delay (CRDSTD) is considered. A periodically intermittent controller is designed such that drive system and corresponding response system can achieve finite-time lag synchronization. By using graph theory and Lyapunov method, two sufficient criteria are presented to guarantee the finite-time lag synchronization of CRDSTD. Moreover, the time of achieving lag synchronization of CRDSTD is estimated. Finally, a numerical example is given to show the effectiveness of the proposed results.

Adaptive Lag Synchronization of Memristive Neural Networks With Mixed Delays

This paper investigates the lag synchronization of memristive neural networks (MNNs) with mixed delays via adaptive control. Based on the switching jump properties of memristors and the assumption that the activation functions are bounded, three lemmas are derived first to deal with the theoretical analysis difficulties caused by the existences of time delays and time lag. By designing a series of suitable adaptive controllers, we prove that the considered MNNs can achieve asymptotic lag synchronization, exponential lag synchronization, and finite-time lag synchronization, respectively. Adaptive control can avoid the large control gains very well, and adaptive control can be used even when the system parameters are unknown. Moreover, extra calculations are not required to determine the appropriate control gains. Numerical simulations are presented to verify the effectiveness of the obtained theoretical results.

Finite-Time Lag Synchronization for Memristive Mixed Delays Neural Networks with Parameter Mismatch

This paper is devoted to study the finite time lag synchronization problem of memristive mixed delays neural networks with switching jumps and parameter mismatch. The main objective of this paper is to design simple linear feedback control such as the drive response systems can realize synchronization in the finite time. Several theoretical aspects are addressed, mean Filippov differential inclusion and set-valued map. Based on the Gronwall’s inequality and properties of differential operation, a new finite time lag synchronization scheme is proposed to guarantee that coupled memristive mixed delays neural networks are in a state of lag synchronization in finite time. In addition, finite lag synchronization criteria of two identical memristive mixed delays neural networks are also considered. Finally, numerical examples are presented to illustrate the effectiveness of the our proposed theorems.

Finite-time lag synchronization of master-slave complex dynamical networks with unknown signal propagation delays

This paper studies the finite-time lag synchronization issue of master-slave complex networks with unknown signal propagation delays by the linear and adaptive error state feedback approaches. The unknown signal propagation delays are fully considered and estimated by adaptive laws. By designing new Lyapunov functional and discontinuous feedback controllers, which involves the estimated error rather than the general synchronization error, sufficient conditions are derived to ensure lag synchronization of the networks within a setting time. It is interesting to discover that the setting time is related to initial values of both the estimated error and the estimated unknown signal propagation delays. Finally, two numerical examples are given to illustrate the effectiveness and correctness of the proposed finite-time lag synchronization criteria.

Finite-time lag synchronization of time-varying delayed complex networks via periodically intermittent control and sliding mode control

In this paper, finite-time lag synchronization of time-varying delayed complex networks is investigated. By designing a periodically intermittent feedback controller and adjusting periodically intermittent control strengths with the updated laws in two parts respectively, we achieve finite-time lag synchronization between two time-varying delayed complex networks. In addition, based on the same finite-time stability theory and the same sliding mode control, we ensure that the trajectory of error system converges to a chosen sliding surface within finite time and remains on it forever. Finally, two examples are given to demonstrate the effectiveness and correctness of the theoretical results obtained here.

Finite-time lag synchronization of delayed neural networks

In this paper, a finite-time lag synchronization of coupled neural networks with time delay is investigated. By means of the Lyapunov stability theory, a feedback controller is designed for achieving lag synchronization between two delayed neural networks systems in finite time. Paper extends some basic results from the area of finite time to time-delay systems. Numerical simulations on coupled Lu neural systems illustrate the effectiveness of the results.