摘要：
Hopfield neural networks are favored by academia and industrial fields due to their abundant dynamics. In this paper, the dynamical behavior of a small Hopfield neural network (HNN) simultaneously stimulated by electromagnetic radiation and multi-level-logic pulse is investigated. Firstly, a modified HNN with three neurons is presented by selecting appropriate synapse weight coefficients. And the system model of the HNN under electromagnetic radiation and an electrical pulse is constructed. Then its equilibrium stabilities and nonlinear dynamical phenomena are analyzed by using numerical analysis methods including phase portraits, Lyapunov exponents, and bifurcation diagrams. The research results show that the neural network affected by electromagnetic radiation and a multi-level-logic pulse signal can generate chaotic multi-scroll attractors, which has not been observed in the previous investigation for the Hopfield-type neural networks. In addition, the number of the scroll can be easily changed by adjusting the electrical pulse signal. Circuit simulations based on the designed neural network circuit are carried out to confirm the numerical simulations. Finally, an HNN-based image encryption scheme is designed from the perspective of engineering applications. Performance evaluations demonstrate that the proposed image cryptosystem has good security.
关键词：
3D Navier-Stokes-Voigt equations;admissible trajectories set;admissible control set;feedback control;time optimal control
摘要：
In this article, we discuss a time optimal feedback control for asymmetrical 3D Navier–Stokes–Voigt equations. Firstly, we consider the existence of the admissible trajectories for the asymmetrical 3D Navier–Stokes–Voigt equations by using the well-known Cesari property and the Fillippove’s theorem. Secondly, we study the existence result of a time optimal control for the feedback control systems. Lastly, asymmetrical Clarke’s subdifferential inclusions and asymmetrical 3D Navier–Stokes–Voigt differential variational inequalities are given to explain our main results.
作者机构：
College of Science, Hunan City University, Yiyang, P. R. China;Department of Mathematics, Huzhou University, Huzhou, P. R. China;[Ghaffar, Abdul] Department of Mathematics, Faculty of Science, Ghazi University, D. G. Khan, Pakistan;[Ghani, Muhammad Usman] Department of Mathematics, Khawaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, Punjab, Pakistan;Department of Computer Engineering, Biruni University, Istanbul, Turkey
通讯机构：
[Mustafa Inc] D;Department of Computer Engineering, Biruni University, Istanbul, Turkey<&wdkj&>Department of Medical Research, China Medical University, Taichung, Taiwan
关键词：
Zagreb polynomials;Zagreb indices;benzenoid triangular system;benzenoid Hourglass system;05C07;05C09;05C31;05C76;05C99
摘要：
In this article, we study benzenoid Triangular system and benzenoid Hourglass system and we compute Zagreb polynomials for benzenoid Triangular system and benzenoid Hourglass system and from these Zagreb polynomials we catch up degree based Zagreb indices.
作者机构：
[Yan, Rian] Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.;[Zhao, Yige] Univ Jinan, Sch Math Sci, Jinan 250022, Peoples R China.
通讯机构：
[Zhao, YG ] U;[Yan, R ] H;Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.;Univ Jinan, Sch Math Sci, Jinan 250022, Peoples R China.
摘要：
In this paper, a class of nonlinear fractional differential equations with periodic boundary condition is investigated. Although the nonlinearity of the equation and the Green's function are sign-changing, the results of the existence and nonexistence of positive solutions are obtained by using the Schaefer's fixed-point theorem. Finally, two examples are given to illustrate the main results.
摘要：
In the past ten years, networking experts have been more concerned about the rising energy consumption of communication networks. The software-defined networks approach is a way to make diverse and complicated network topologies simpler, more manageable, more adaptable, and more effective, including wireless body area networks. In order to streamline network administration, save operational costs, and promote innovation, software-defined networks are emerging as a new networking architecture that separates the data plane from the control plane. However, despite the importance of this issue, so far, no bibliometric study has been done on this issue. Hence, this study aims to use methods drawn from nature to optimize power usage in software-defined networks. Additionally, a thorough and original categorization of energy-efficient solutions has been offered. During the bibliographic review, the sections of interest of researchers and some bibliographic information in the form of statistical information are expressed. Therefore, searching and selecting relevant keywords are done using the VOSviewer tool. The data is extracted from valid databases. Guidelines for future research on software-defined networks are derived based on the existing research projects' findings and the gaps and constraints that have been found. The results showed that the algorithms inspired by nature were successful in striking a balance among resource usage, energy consumption, and network performance.
作者机构：
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, China;School of Mathematics and Computational Sciences, Xiangtan University, Xiangtan, China;[Yi Yang] School of Mathematics, Hunan City University, Yiyang, China;[Su-Han Zhong] Department of Mathematics, Texas A &M University, College Station, USA;[Liu Yang] Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, China<&wdkj&>School of Mathematics and Computational Sciences, Xiangtan University, Xiangtan, China
通讯机构：
[Liu Yang] H;Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, China<&wdkj&>School of Mathematics and Computational Sciences, Xiangtan University, Xiangtan, China
关键词：
Portfolio selection model;High-order moments;Moment-SOS relaxation;Perturbation sample average approximation
摘要：
In this paper, we study the global optimality of polynomial portfolio optimization (PPO). The PPO is a kind of portfolio selection model with high-order moments and flexible risk preference parameters. We introduce a perturbation sample average approximation method, which can give a robust approximation of the PPO in form of linear conic optimization. The approximated problem can be solved globally with Moment-SOS relaxations. We summarize a semidefinite algorithm, which can be used to find reliable approximations of the optimal value and optimizer set of the PPO. Numerical examples are given to show the efficiency of the algorithm.
