Dissipativity and synchronization control of fractional‐order memristive neural networks with reaction‐diffusion terms

This paper deals with the dissipativity and synchronization control of fractional‐order memristive neural networks (FOMNNs) with reaction‐diffusion terms. By means of fractional Halanay inequality, Wirtinger inequality, and Lyapunov functional, some sufficient conditions are provided to ensure global dissipativity and exponential synchronization of FOMNNs with reaction‐diffusion terms, respectively. The underlying model and the obtained results are more general since the reaction‐diffusion terms are first introduced into FOMNNs. The given conditions are easy to be checked, and the correctness of the obtained results is confirmed by a living example.     

Motion of curves and solutions of two multi-component mKdV equations

Two classes of multi-component mKdV equations have been shown to be integrable. One class called the multi-component geometric mKdV equation is exactly the system for curvatures of curves when the motion of the curves is governed by the mKdV flow. In this paper, exact solutions including solitary wave solutions of the two- and three-component mKdV equations are obtained, the symmetry reductions of the two-component geometric mKdV equation to ODE systems corresponding to it’s Lie point symmetry groups are also given. Curves and their behavior corresponding to solitary wave solutions of the two-component geometric mKdV equation are presented.     

Nonlinear measure approach for the robust exponential stability analysis of interval inertial Cohen–Grossberg neural networks

This article is concerned with the existence and robust stability of an equilibrium point that related to interval inertial Cohen–Grossberg neural networks. Such condition requires the existence of an equilibrium point to a given system, so the existence and uniqueness of the equilibrium point are emerged via nonlinear measure method. Furthermore, with the help of Halanay inequality lemma, differential mean value theorem as well as inequality technique, several sufficient criteria are derived to ascertain the robust stability of the equilibrium point for the addressed system. The results obtained in this article will be shown to be new and they can be considered alternative results to previously results. Finally, the effectiveness and computational issues of the two models for the analysis are discussed by two examples. © 2016 Wiley Periodicals, Inc. Complexity 21: 459–469, 2016     

EXACT EXPLICIT SOLUTIONS OF THE NONLINEAR SCHRDINGER EQUATION COUPLED TO THE BOUSSINESQ EQUATION

A system comprised of the nonlinear Schrodinger equation coupled to the Boussinesq equation (S-B equations) which dealing with the stationary propagation of coupled non-linear upper-hybrid and magnetosonic waves in magnetized plasma is proposed. To examine its solitary wave solutions, a reduced set of ordinary differential equations are considered by a simple traveling wave transformation. It is then shown that several new     

Stability analysis of quaternion‐valued Cohen‐Grossberg neural networks

In this paper, by starting from basic quaternion algebra properties and algorithms, a quaternion‐valued Cohen‐Grossberg neural network was derived, subsequently, several new sufficient conditions are derived to ensure existence and global asymptotic stability (GAS) and global exponential stability (GES) of the equilibrium point (EP) for quaternion‐valued Cohen‐Grossberg neural networks. The obtained criteria can be checked easily in practice and have a distinguished feature from previous studies. Finally, we have numerical evidences that the mathematical system and the conclusions presented are validated.     

硅掺杂的氮化硼纳米管对氯化氰吸附性能的理论研究

为了探索氮化硼纳米管(BNNT)在化学传感器件领域的潜在应用,我们利用密度泛函理论研究了(8,0)单壁BNNT和硅掺杂的(8,0)BNNT对毒性气体氯化氰分子(ClCN)的吸附性能.结果表明,硼位或氮位硅掺杂的BNNT,均对ClCN分子存在较强的化学吸附,而纯氮化硼纳米管对ClCN仅有较弱的物理吸附.态密度的计算进一步表明硅掺杂使纳米管费米能级附近的电子结构发生显著变化,由于杂化态的引入,使带隙明显减小,增强了对毒性ClCN分子的吸附敏感性.硅掺杂的BNNT有望成为检测毒性ClCN分子的潜在资源.     

Detection of cortisol at a gold nanoparticle|Protein G-DTBP-scaffold modified electrochemical immunosensor

An ultrasensitive electrochemical immmunosensor was demonstrated to be capable of detecting the hormone cortisol down to concentrations as low as 16 pg mL(-1). In addition, the immunosensor displayed a sensitivity of 1.6 μA pg(-1) mL(-1) and a linear range up to ～2500 pg mL(-1) of cortisol. This immunosensor was constructed based on a Au nanoparticle|dimethyl 3,3'-dithiobispropionimidate·2HCl (DTBP)-Protein G scaffold-modified Au electrode. In this work, the Au nanoparticles were used to increase the electrochemically active surface area by 28% (with a standard deviation of 3%) to enhance the quantity of the Protein G scaffold on the electrode. Thiolation of Protein G by DTBP aided in avoiding the confirmation change of Protein G, while this Protein G-DTBP component offered an orientation-controlled immobilisation of the capture antibody on the Au electrode. In this immunosensor, a monoclonal anti-cortisol capture antibody was optimally aligned by the scaffold before a competitive immunoassay between sample cortisol and a horseradish peroxidase-labelled cortisol conjugate was conducted. For quantitative analysis, square wave voltammetry was used to monitor the reduction current of benzoquinone produced from a horseradish peroxidase catalysed reaction. The improved analytical performance of our immunosensor was attributed to the synergetic effect of Au nanoparticles and the Protein G-DTBP scaffold.     

Dissipativity analysis of memristive neural networks with time‐varying delays and randomly occurring uncertainties

Dissipativity theory is a very important concept in the field of control system. In this paper, we pay attention to the problem of dissipativity analysis of memristive neural networks with time‐varying delay and randomly occurring uncertainties(ROUs). Under the framework of Filippov solution, differential inclusion theory, by employing a proper Lyapunov functional, and some inequality techniques, the dissipativity criteria are obtained in terms of LMIs. It should be noteworthy that the uncertainty terms as well as the ROUs are separately taken into consideration, in which the uncertainties are norm‐bounded and the ROUs obey certain mutually uncorrelated Bernoulli‐distributed white noise sequences. Finally, the effectiveness of the proposed method will be verified via numerical example. Copyright © 2015 John Wiley & Sons, Ltd.     

Darboux transformation and soliton solutions of a nonlocal Hirota equation

Starting from local coupled Hirota equations,we provide a reverse space-time nonlocal Hirota equation by the symmetry reduction method known as the Ablowitz–Kaup–Newell–Segur scattering problem.The Lax integrability of the nonlocal Hirota equation is also guaranteed by existence of the Lax pair.By Lax pair,an n-fold Darboux transformation is constructed for the nonlocal Hirota equation by which some types of exact solutions are found.The solutions with specific properties are distinct from those of the local Hirota equation.In order to further describe the properties and the dynamic features of the solutions explicitly,several kinds of graphs are depicted.