We study the dynamics of some Newton-type iterative methods when they are applied of polynomials degrees two and three. The methods are free of high-order derivatives which are the main limitation of the classical high-order iterative schemes. The iterative schemes consist of several steps of damped Newton's method with the same derivative. We introduce a damping factor in order to reduce the bad zones of convergence. The conclusion is that the damped schemes become real alternative to the classical Newton-type method since both chaos and bifurcations of the original schemes are reduced. Therefore, the new schemes can be utilized to obtain good starting points for the original schemes.

We investigate the global $\mu$-stability in the mean square of impulsive stochastic neural networks with unbounded time-varying delays and continuous distributed delays. By choosing an appropriate Lyapunov-Krasovskii functional, a novel robust stability condition, in the form of linear matrix inequalities, is derived. These sufficient conditions can be tested by MATLAB LMI software packages. The results extend and improve the earlier publication. Two numerical examples are provided to illustrate the effectiveness of the obtained theoretical results.

In order to improve the precision of Strapdown Inertial Navigation System (SINS) and reduce the complexity of the traditional calibration method, a novel calibration and compensation scheme is proposed. An optimization calibration method with four-direction rotations is designed to calculate all error coefficients of Ring Laser Gyroscope (RLG) SINS in a series of constant temperatures. According to the actual working environment, the temperature errors of RLG SINS are compensated by a nonlinear interpolation compensation algorithm. The experimental results show that the inertial navigation errors of the proposed method are reduced.

Wireless mesh networks (WMNs) are a promising networking paradigm for next generation wireless networking system. Power control plays a vital role in WMNs and is realized to be a crucial step toward large-scale WMNs deployment. In this paper, we address the problem of how to allocate the power for both optimizing quality of service (QoS) and saving the power consumption in WMNs based on the game theory. We first formulate the problem as a noncooperative game, in which the QoS attributes and the power of each node are defined as a utility function, and all the nodes attempt to maximize their own utility. In such game, we correlate all the interfering nodes to be an interfering object and the receiving node to be the interfering object's virtual destination node. We then present an equilibrium solution for the noncooperative game using Stackelberg model, and we propose an iterative, distributed power control algorithm for WMNs. Also, we conduct numeric experiments to evaluate the system performance, our results show that the proposed algorithm can balance nodes to share the limited network resources and maximize total utility, and thus it is efficient and effective for solving the power control problem in WMNs.

A finite volume element method for approximating the solution to two-dimensional Burgers equation is presented. Upwind technique is applied to handle the nonlinear convection term. We present the semi-discrete scheme and fully discrete scheme, respectively. We show that the schemes are convergent to order one in space in $L^{\mathrm{2}}$-norm. Numerical experiment is presented finally to validate the theoretical analysis.

This paper introduces a new approach to design Model-Free Adaptive Controller (MFAC) using adaptive fuzzy procedure as a feedback linearization based on output error. The basic idea is to transfer the control signal to an appropriate surface and then, depending on the output error of system, the control signal changes around this surface. Some examples are provided as well to illustrate the efficiency of the proposed approach. The obtained simulation results have shown good performances of the proposed controller.

Compound controller which consists of CMAC network and PID network is mainly used in control system, especially in robot control. It can realize nonlinear tracking control of the real-time dynamic trajectory and possesses good approximation effect. According to the structure and principle of the compound controller, memristor is introduced to CMAC network to be a compound controller in this paper. The new PID controller based on memristive CMAC network is built up by replacing the synapse in the original controller by memristors. The effect of curve approximation is obtained by MATLAB simulation experiments. This network improves the response and learning speed of the system and processes better robustness and antidisturbance performance.

The main purpose is to investigate both deterministic and stochastic bifurcations of the catalytic CO oxidation. Firstly, super- and subcritical bifurcations are determined by the signs of the Poincaré-Lyapunov coefficients of the center manifold scalar bifurcation equations. Secondly, we explore the stochastic bifurcation of the catalytic CO oxidation on Ir(111) surfaces with multiple delays according to the qualitative changes in the invariant measure, the Lyapunov exponent, and the stationary probability density of system response. Some new criteria ensuring stability and stochastic bifurcation are obtained.

A new symplectic chaos synchronization of chaotic systems with uncertain chaotic parameters is studied. The traditional chaos synchronizations are special cases of the symplectic chaos synchronization. A sufficient condition is given for the asymptotical stability of the null solution of error dynamics and a parameter difference. The symplectic chaos synchronization with uncertain chaotic parameters may be applied to the design of secure communication systems. Finally, numerical results are studied for symplectic chaos synchronized from two identical Lorenz-Stenflo systems in three different cases.

Fuzzy electronic circuit (FEC) is firstly introduced, which is implementing Takagi-Sugeno (T-S) fuzzy chaotic systems on electronic circuit. In the research field of secure communications, the original source should be blended with other complex signals. Chaotic signals are one of the good sources to be applied to encrypt high confidential signals, because of its high complexity, sensitiveness of initial conditions, and unpredictability. Consequently, generating chaotic signals on electronic circuit to produce real electrical signals applied to secure communications is an exceedingly important issue. However, nonlinear systems are always composed of many complex equations and are hard to realize on electronic circuits. Takagi-Sugeno (T-S) fuzzy model is a powerful tool, which is described by fuzzy IF-THEN rules to express the local dynamics of each fuzzy rule by a linear system model. Accordingly, in this paper, we produce the chaotic signals via electronic circuits through T-S fuzzy model and the numerical simulation results provided by MATLAB are also proposed for comparison. T-S fuzzy chaotic Lorenz and Chen-Lee systems are used for examples and are given to demonstrate the effectiveness of the proposed electronic circuit.

In the real business world, player sometimes would offer a limiter to their output due to capacity constraints, financial constraints, or cautious response to uncertainty in the world. In this paper, we modify a duopoly game with bounded rationality by imposing lower limiters on output. Within our model, we analyze how lower limiters have an effect on dynamics of output and give proof in theory why adding lower limiters can suppress chaos. We also explore the numbers of the equilibrium points and the distribution of conditioned equilibrium points. Stable region of the conditioned equilibrium is discussed. Numerical experiments show that the output evolution system having lower limiters becomes more robust than without them, and chaos disappears if the lower limiters are big enough. The local or global stability of the conditional equilibrium points provides a theoretical basis for the limiter control method of chaos in economic systems.

We focus on the cluster synchronization problem for a kind of general networks with nondelayed and delayed coupling. Based on the pinning control scheme, a small fraction of the nodes in each cluster are pinned for successful control, and the states of the whole dynamical networks can be globally forced to the objective cluster states. Sufficient conditions are derived to guarantee the realization of the cluster synchronization pattern for all initial values by means of the Lyapunov stability theorem and linear matrix inequalities (LMIs). By using the adaptive update law, relative smaller control gains are obtained, and hence the control cost can be substantially lower. Numerical simulations are also exploited to demonstrate the effectiveness and validity of the main result.

The synchronization problem of chaotic fuzzy cellular neural networks with mixed delays is investigated. By an impulsive integrodifferential inequality and the Itô's formula, some sufficient criteria to synchronize the networks under both impulsive and stochastic perturbations are obtained. The example and simulations are given to demonstrate the efficiency and advantages of the proposed results.

When the dimension of covariates in the regression model is high, one usually uses a submodel as a working model that contains significant variables. But it may be highly biased and the resulting estimator of the parameter of interest may be very poor when the coefficients of removed variables are not exactly zero. In this paper, based on the selected submodel, we introduce a two-stage remodeling method to get the consistent estimator for the parameter of interest. More precisely, in the first stage, by a multistep adjustment, we reconstruct an unbiased model based on the correlation information between the covariates; in the second stage, we further reduce the adjusted model by a semiparametric variable selection method and get a new estimator of the parameter of interest simultaneously. Its convergence rate and asymptotic normality are also obtained. The simulation results further illustrate that the new estimator outperforms those obtained by the submodel and the full model in the sense of mean square errors of point estimation and mean square prediction errors of model prediction.

We investigate the lag synchronization of coupled neural networks with time delay. Some sufficient conditions for lag synchronization will be derived by using Lyapunov stability theory and intermittent control. Compared to existing results, some less conservative conditions are derived to guarantee the stabilization of error system. The analytical results are confirmed by numerical simulations.

We present a theoretical analysis of processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with cross-diffusion in a Harrison-type predator-prey model. We analyze the global behaviour of the model by establishing a Lyapunov function. We carry out the analytical study in detail and find out the certain conditions for Turing’s instability induced by cross-diffusion. And the numerical results reveal that, on increasing the value of the half capturing saturation constant, the sequences “spots → spot-stripe mixtures → stripes → hole-stripe mixtures → holes” are observed. The results show that the model dynamics exhibits complex pattern replication controlled by the cross-diffusion.

The memristor (resistor with memory), as the fourth fundamental circuit element, is a nonvolatile nanoelectronic device and holds great promise for VLSI applications. It was suggested that the meminductor (ML, inductor with memory) circuit can be built by memristor emulators. This paper further addresses the transformation mechanism in terms of constitutive relation from the memristor to the meminductor and then designs an MR-ML mutator to achieve MR-ML transformation. We also present the mutator’s SPICE model and analyze the simulation results.