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In this paper, the problem of synchronization for neutral-type quaternion-valued neural networks (NQVNNs) with mixed delays is investigated. By making full use of the information of the time-delay state, a linear feedback controller and a novel nonlinear feedback controller are constructed to research the global synchronization and finite-time synchronization of the system respectively. In the case where the activation function of the network is not required to be separated into two complex parts or four real parts, the sufficient conditions of synchronization of NQVNNs are acquired based on establishing appropriate Lyapunov-Krasovskii functional, applying the synchronization method of drive-response and some inequality techniques. The obtained delay-dependent synchronization results are less conservative than some existing ones via numerical example comparisons. Two numerical examples with simulations are provided to verify the effectiveness of the obtained results.

Chaotic or hyperchaotic systems are widely applied in many engineering fields, such as information security, cryptography and secure communication. In order to implement better performance, it is necessary to carry out exhaustive studies on the dynamic properties of the systems. This paper presents a deep investigation on complex behaviors in a system having very strong hyperchaos which has great potential application value. By a serial of numerical methods, such as phase portraits, Lyapunov exponents and analysis of attraction basin, it is found out that co-existing of multiattractor and chaotic transition simultaneously exist. Moreover, some new patterns are also observed. These complex dynamics are helpful to understand the behaviors of the system and will broaden the application scenarios of this system.

In chaos engineering, especially for chaos-based communication, chaotic systems require high complex, strong robustness and well-distributed bandwidth. In this paper, we present a new four-dimensional (4D) hyperchaotic system, which satisfies these three significant properties at the same time. Instead of traditional evaluation method of the positive Lyapunov exponents, the complexity of the system is measured by the topological entropy. We find out that it has much larger topological entropy and Kaplan–Yorke dimension compared with the systems reported before, therefore it may have better engineering application value.

Summary Underground gas storage (UGS) is an important segment in China's gas market. Because of the supply-and-demand misbalance of natural gas, the gas in underground storage is made available during the peak winter season. In the west of China, the Hutubi dry-gas field is to be used for UGS with a storage capacity of 4.5 × 109 m3. A total of 37 wells will be drilled with 30 natural-gas-injection/-withdrawal wells, five observation wells, and two water-injection wells. UGS relies on proper wellbore construction and the sealing function of the caprock. The selection of the type of cement is crucial to having a healthy well that will last to meet the gas-storage need of 30 years under high-intensity injection. The gas injection and withdrawal will induce different stresses on the cement sheath and may destroy the seal by either debonding (microannulus) or cracking; an effective cement system is required to prevent the leakage of the gas and flow through the caprock. A specialized cement technology was identified as a solution to UGS and was deployed successfully in the Hutubi field with good results. The cement selected had to meet the pressure and temperature challenges associated with UGS, and a methodology was established to qualify the new sealant. Case histories of three wells illustrate the steps taken in cementing UGS wells in the field.

In this paper, the problem of function projective synchronization is investigated for complex networks with stochastic effects. A hybrid feedback control method is designed to achieve function projective synchronization for the complex networks. Using Gronwally' inequality, we obtain some conditions to guarantee that the complex networks can realize mean square synchronization and mean square exponential synchronization, respectively.

The problem of mean square bounded-input-bounded-output (BIBO) stability for the stochastic delay systems with nonlinear perturbations is investigated in this paper. Using the Razumikhin technique combined with comparison principle, several novel BIBO mean square stability criteria are established. A numerical example is given to illustrate the effectiveness of our result.

This paper is concerned with the problem of the stochastic admissibility for a class of nonlinear singular Markovian jump systems with time-delay by employing the free-weighting matrix method and the Lyapunov functional method. The singular matrices Er(t)in the discussed system are mode-dependent. A sufficient condition is presented to guarantee the considered system to be stochastically admissible. The proposed result is formulated in terms of linear matrix inequalities(LMIs). A numerical example is provided to verify the effectiveness of the obtained method.

The problem of the stochastic admissibility for a class of nonlinear singular Markovian jump systems with time-delay and partially unknown transition probabilities is discussed in this note. The considered singular matrices Er(t) in the discussed system are mode-dependent. By using the free-weighting matrix method and the Lyapunov functional method, a sufficient condition which guarantees the considered system to be stochastically admissible is presented in the form of linear matrix inequalities(LMIs). Finally, a numerical example is given to show the effectiveness of the presented method.

This paper deals with the problem of fault detection for Markov jump systems (MJSs) with time-varying delays and partly unknown transition probabilities. The aim of this paper is to design a fault detection filter such that the filtering error system is stochastically asymptotically stable with an attenuation level. By using the Lyapunov-Krasovskii functional, a sufficient condition for the existence of the desired fault detection filter is formulated in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed main results.

In this paper, the mean square asymptotical stability is investigated for a class of discrete-time stochastic systems with time-varying delays and norm-bounded uncertainties,a numerical example is presented to show the usefulness of the derived LMI-based stability condition.

This paper revisits the problem of stability analysis for discrete-time stochastic neural networks (DSNNs) with mixed time-varying delays in the state. Here the mixed time delays are assumed to be discrete and distributed time delays and the uncertainties are assumed to be time varying norm bounded parameter uncertainties. A new delay-dependent stability criterion is presented by constructing a novel Lyapunov-Krasovskii functional and utilizing the delay partitioning idea and free-weighting matrix approach, Which is less conservative than the existing ones. This criterion can be developed in the frame of convex optimization problems and then solved via standard numerical software. These conditions are formulated in the forms of linear matrix inequalities, which feasibility can be easily checked by using Matlab LMI Toolbox.

Delay-dependent stability of descriptor neutral systems with mixed delays is investigated in this paper. Based on descriptor system approach, some new delay-dependent stability and robust stability criteria are established in terms of a operator and linear matrix inequalities(LMIs). Lyapunov-Krasovskii functional and Leibniz-Newton formula are applied to find the stability results.

The problem of delay-probability-distribution-dependent stability analysis for a class of discrete-time stochastic delayed neural networks (DSNNs) with mixed time delays is investigated. Here the mixed time delays are assumed to be discrete and distributed time delays and the uncertainties are assumed to be time varying norm bounded parameter uncertainties. The information of the probability distribution of the time-varying delay is considered and transformed into parameter matrices of the transferred DSNN model, in which the time-varying delay is characterized by introducing a Bernoulli stochastic variable. By constructing a new augmented Lyapunov-Krasovskii functional and introducing some new analysis techniques, a novel delay-probability-distribution-dependent stable criterion for the DSNN to be stable in the mean square sense are derived. These criteria are formulated in the forms of linear matrix inequalities.

The global exponential stability for switched neutral systems with time-varying delays and nonlinear perturbations is investigated in this paper. LMI-based delay-dependent criterion is proposed to guarantee exponential stability for our considered systems under any switched signal. Lyapunov-Krasovskii functional and Leibniz-Newton formula are applied to find the stability results. Free weighting matrix and linear matrix inequality (LMI) approaches are used to solve the proposed conditions.

In this paper, the BIBO stabilization problem for a class of fuzzy large-scale systems is investigated. Based on the Lyapunov function and the LMI approach, sufficient conditions for the solvability of this problem are proposed in terms of LMIs, and an explicit expression of the desired controller is readily given when these LMIs are feasible.

This paper investigates the robust stability of uncertain neutral system with time-varying delay and nonlinear uncertainties. By using Lyapunov method and linear matrix inequality technology, a new delay-dependent stability criteria is obtained and formulated in terms of linear matrix inequalities (LMIs) which can be easy to check the robust stability of the considered systems. Numerical examples are given to indicate significant improvements over some existing results.

This article studies the neutral system with time-varying delay and uncertainties. Novel stability criteria of the neutral system are derived by using Lyapunov method and linear matrix inequality technology which can be easily solved by efficient convex optimization algorithms. Some numerical examples are given to illustrate our theoretical results.

In this paper, we mainly study the Lyapunov asymptotical stability of linear and interval linear fractional order neutral systems with time delay. By applying the characteristic equations of these two systems, some simple sufficient Lyapunov asymptotical stability conditions are deserved, which are quite different from other ones in literature. In addition, some numerical examples are provided to demonstrate the effectiveness of our results.

Underground gas storage is an important segment in China’s gas market. Because of the supply and demand misbalance of natural gas, the gas in underground storage is made available during the peak winter season. In the west of China, the Hutubi dry gas field is to be used for underground gas storage with a storage capacity of 4.5 × 109 m3. A total of 37 wells will be drilled with 30 natural gas injection/withdrawal wells, 5 observation wells, and 2 water injection wells. Underground gas storage relies on proper wellbore construction and the sealing function of the caprock. The selection of the type of cement is crucial to having a healthy well that will last to meet the gas storage need of 30 years under high intensity injection. The gas injection and withdrawal will induce different stresses on the cement sheath and may destroy the seal by either debonding (microannulus) or cracking; an effective cement system is required to prevent leakage of the gas and flow through the caprock. A specialized cement technology was identified as a solution to underground gas storage and was deployed successfully in the Hutubi field with great results. The cement selected had to meet the pressure and temperature challenges associated with the underground gas storage, and a methodology was established to qualify the new sealant. Case histories of three wells illustrate the steps taken in cementing UGS wells in the field.

In this paper, a viral infection SVI model with lytic immune response is studied. What's more, in order to control the quantity of the virus population, periodic medication strategy is introduced to the classical SVI model. By some mathematical analysis techniques, an important threshold

In this paper, some brief sufficient conditions for the stability of FO-LTI systems dαx(t) dtα = Ax(t) with the fractional order are investigated when the matrix A and the fractional order α are uncertain or both α and A are uncertain, respectively. In addition, we also relate the stability of a fractional-order system with order 0 < α ≤ 1 to the stability of its equivalent fractional-order system with order 1 ≤ β < 2, the relationship between α and β is presented. Finally, a numeric experiment is given to demonstrate the effectiveness of our results.

A new nonlinear discrete inequality in two variables is discussed. It generalizes some known results and can be used as handy tool in the study of the existence, uniqueness, boundedness and many other properties of the solution of certain partial difference equation. An example to show boundedness of solution of a difference value problem is also given.

In this paper, the absolute stability of a new class of Takagi-Sugeno (T-S) fuzzy Lurie control systems with multiple time-delays is investigated. By utilizing the Lyapunov stability theory and the linear matrix inequality (LMI) approach, a novel delay-dependent absolutely stable condition is derived. In addition, by using Simulink toolbox in MATLAB, a simulation example is provided to demonstrate effectiveness of the proposed result.

The problem of exponential P stability of neutral stochastic differential equations with discrete and distributed time verying delays is investigated. The authors gave a sufficient condition of exponential P stability by the fixed point theory rather than the Lyapunov functions. Since more general form of system is considered, this paper improves Luo Jiaowan's results.

This paper investigates the stability of a class of delayed neural networks with impulses. By means of Lyapunov direct method, the new sufficient conditions for exponential stability of the systems are derived.

In this paper, the global exponential stability for a class of impulsive cellular neural networks with discrete and distributed time-varying delays is considered. The results are based on the Lyapunov-Krasovskii functional stability analysis for differential equations and the linear matrix inequality (LMI) optimization approach. Some numerical examples are given to show the effectiveness of our results.

This letter concerns with robust exponential stability of stochastic neural networks with Markovian switching. By applying Lyapunov functional method, a sufficient stabilization condition is developed in terms of matrix inequalities. The result is also compared with the previously reported results in the literature. Finally, one simulation example is provided to illustrate the effectiveness of the results developed.

She gave the new sufficient conditions for the exponential stability of BAM neural networks with distribute delays. The analysis of the stability of the equilibrium point had focused on establishing a relationship between the networks parameters of neural networks model independent of the delay parameters.

In this paper, asymptotic stability for a new type of neutral delay neural networks systems is investigated. Stability criteria are presented by using Lyapunov method and linear matrix inequalities (LMIs) which can be easily solved by LMI Toolbox in Matlab.

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.

In this paper, the exponential stability problems for fuzzy cellular neural networks with time-varying delays are investigated. We first give a condition of the existence and uniquen-ess uniqueness of the equilibrium point for systems under consideration. Then, using the methods of varying parametric and inequality analysis technique, we obtained exponential stability criteria and estimation of the convergence rate for such systems.