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现代非线性理论与应用(英文)最新文献

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Local Stability Analysis and Bifurcations of a Discrete-Time Host-Parasitoid Model 离散时间寄主-寄主模型的局部稳定性分析和分岔
Pub Date : 2020-06-10 DOI: 10.4236/ijmnta.2020.92002
T. Azizi
In this paper, we examine a discrete-time Host-Parasitoid model which is a non-dimensionalized Nicholson and Bailey model. Phase portraits are drawn for different ranges of parameters and display the complicated dynamics of this system. We conduct the bifurcation analysis with respect to intrinsic growth rate r and searching efficiency a. Many forms of complex dynamics such as chaos, periodic windows are observed. Transition route to chaos dynamics is established via period-doubling bifurcations. Conditions of occurrence of the period-doubling, Neimark-Sacker and saddle-node bifurcations are analyzed for b≠a where a,b are searching efficiency. We study stable and unstable manifolds for different equilibrium points and coexistence of different attractors for this non-dimensionalize system. Without the parasitoid, the host population follows the dynamics of the Ricker model.
本文研究了一种非量纲化的Nicholson - Bailey模型——离散寄主-拟寄主模型。在不同的参数范围内绘制了相位图,显示了系统复杂的动力学特性。我们对固有增长率r和搜索效率a进行了分岔分析。观察到许多形式的复杂动力学,如混沌、周期窗。通过倍周期分岔建立了混沌动力学的过渡路径。分析了b≠a时倍周期分岔、neimmark - sacker分岔和鞍节点分岔发生的条件,其中a、b为搜索效率。研究了该非量纲化系统不同平衡点下的稳定流形和不稳定流形,以及不同吸引子的共存。没有拟寄生物,寄主种群遵循Ricker模型的动态。
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引用次数: 0
Feedback Systems on a Reflexive Banach Space—Linearization 自反Banach空间上的反馈系统——线性化
Pub Date : 2020-06-10 DOI: 10.4236/ijmnta.2020.92003
M. Khelifa
The aim of our work is to formulate and demonstrate the results of the normality, the Lipschitz continuity, of a nonlinear feedback system described by the monotone maximal operators and hemicontinuous, defined on real reflexive Banach spaces, as well as the approximation in a neighborhood of zero, of solutions of a feedback system [A,B] assumed to be non-linear, by solutions of another linear, This approximation allows us to obtain appropriate estimates of the solutions. These estimates have a significant effect on the study of the robust stability and sensitivity of such a system see [1] [2] [3]. We then consider a linear FS , and prove that, if ; , with the respective solutions of FS’s [A,B] and corresponding to the given (u,v) in . There exists,, positive real constants such that, . These results are the subject of theorems 3.1, ... , 3.3. The proofs of these theorems are based on our lemmas 3.2, ... , 3.5, devoted according to the hypotheses on A and B, to the existence of the inverse of the operator I+BA and . The results obtained and demonstrated along this document, present an extension in general Banach space of those in [4] on a Hilbert space H and those in [5] on a extended Hilbert space .
我们工作的目的是公式化和证明由实自反Banach空间上定义的单调极大算子和半连续算子描述的非线性反馈系统的正规性、Lipschitz连续性的结果,以及假设为非线性的反馈系统[a,B]的解在零邻域内由另一个线性的解近似的结果,这种近似使我们能够获得对解的适当估计。这些估计对此类系统的鲁棒稳定性和灵敏度的研究具有重要影响,参见[1][2][3]。然后我们考虑线性FS,并证明,如果,具有FS[A,B]的相应解,并且对应于中的给定(u,v)。存在,,正实常数,这样。这些结果是定理3.1,…,3.3的主题。这些定理的证明是基于我们的引理3.2,…,3.5,根据关于A和B的假设,致力于算子I+BA和的逆的存在性。根据本文获得并证明的结果,在一般Banach空间中给出了[4]中的结果在Hilbert空间H上的扩展和[5]中的那些结果在扩展Hilbert空间上的扩展。
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引用次数: 0
Forecasting-Based Adaptive Optimized Dispatch in Smart Grid Online 基于预测的智能电网在线自适应优化调度
Pub Date : 2020-02-10 DOI: 10.4236/ijmnta.2020.91001
Q. Jiang, Dan Hu, Du-yi He
The power grid is a fusion of technologies in energy systems, and how to adjust and control the output power of each generator to balance the load of the grid is a crucial issue. As a platform, the smart grid is for the convenience of the implementation of adaptive control generators using advanced technologies. In this paper, we are introducing a new approach, the Central Lower Configuration Table, which optimizes dispatch of the generating capacity in a smart grid power system. The dispatch strategy of each generator in the grid is presented in the configuration table, and the scenario consists of two-level agents. A central agent optimizes dispatch calculation to get the configuration table, and a lower agent controls generators according to the tasks of the central level and the work states during generation. The central level is major optimization and adjustment. We used machine learning to predict the power load and address the best optimize cost function to deal with a different control strategy. We designed the items of the cost function, such as operations, maintenances and the effects on the environment. Then, according to the total cost, we got a new second-rank-sort table. As a result, we can resolve generator’s task based on the table, which can also be updated on-line based on the environmental situation. The signs of the driving generator’s controller include active power and system’s f. The lower control level agent carries out the generator control to track f along with the best optimized cost function. Our approach makes optimized dispatch algorithm more convenient to realize, and the numerical simulation indicates the strategy of machine learning forecast of optimized power dispatch is effective.
电网是能源系统技术的融合,如何调整和控制每台发电机的输出功率以平衡电网负载是一个关键问题。智能电网作为一个平台,是为了方便发电机采用先进技术实现自适应控制。在本文中,我们介绍了一种新的方法,即中央下配置表,它可以优化智能电网电力系统中的发电量调度。配置表中给出了电网中每个发电机的调度策略,该场景由两级代理组成。中央代理优化调度计算得到配置表,下级代理根据中央级的任务和生成过程中的工作状态控制生成器。中央层面是重大优化调整。我们使用机器学习来预测电力负载,并解决最佳优化成本函数,以处理不同的控制策略。我们设计了成本函数的项目,如操作、维护和对环境的影响。然后,根据总成本,我们得到了一个新的二阶排序表。因此,我们可以基于该表来解决发电机的任务,该表也可以根据环境情况在线更新。驱动发电机控制器的标志包括有功功率和系统的f。较低控制级别的代理执行发电机控制以跟踪f以及最佳优化成本函数。该方法使优化调度算法更易于实现,数值模拟表明,优化调度的机器学习预测策略是有效的。
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引用次数: 0
Dynamics of a Stochastic Delayed Predator-Prey System with Beddington-DeAngelis Functional Response 具有Beddington-DeAngelis功能响应的随机延迟捕食-食饵系统动力学
Pub Date : 2019-11-13 DOI: 10.4236/ijmnta.2019.84007
Mengwei Li, Yuanfu Shao, Yafei Yang
This paper is concerned with a stochastic predator-prey system with Beddington-DeAngelis functional response and time delay. Firstly, we show that this system has a unique positive solution as this is essential in any population dynamics model. Secondly, the validity of the stochastic system is guaranteed by stochastic ultimate boundedness of the analyzed solution. Finally, by constructing suitable Lyapunov functions, the asymptotic moment estimation of the solution was given. These properties of the solution can provide theoretical support for biological resource management.
研究了一类具有Beddington-DeAngelis函数响应和时滞的随机捕食系统。首先,我们证明了这个系统有一个唯一的正解,这在任何种群动力学模型中都是必不可少的。其次,通过分析解的随机极限有界性来保证随机系统的有效性。最后,通过构造合适的Lyapunov函数,给出了解的渐近矩估计。该溶液的这些特性可为生物资源管理提供理论支持。
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引用次数: 0
Analyzing the Impact of Bapco 5 MW Solar PV Grid-Connected Project on Bahrain’s Outlook for Energy-Mix Production 分析Bapco 5兆瓦太阳能光伏并网项目对巴林能源组合生产前景的影响
Pub Date : 2019-08-08 DOI: 10.4236/IJMNTA.2019.83006
N. Alnaser, W. Alnaser
The impact of Bapco 5 MW solar PV grid-connected project on Bahrain’s outlook for clean energy and energy-mix production was analyzed since solar electricity obtained from PV installation is considered as a non-linear system. Several positive impacts were counted. These impacts were on business, economy, environment, research, green jobs creation and rooftop installation and other large-scale installation. This project had attracted public, investors, developers to invest in similar projects in the Kingdom of Bahrain; especially it is an environmentally friendly and smart technology. This innovative smart grid-connected 5 MW solar PV power plant is enough to electrify 500 houses @ 10 kW and had answered lots of frustrating questions such as the effect of dust on PV performance, need of man-made cleaning compared to naturally cleaned PV panels, reliability of the system, greenhouse gases reduction and pay-back period.
分析了Bapco 5 MW太阳能光伏并网项目对巴林清洁能源和能源混合生产前景的影响,因为从光伏安装中获得的太阳能电力被认为是一个非线性系统。统计了几个积极影响。这些影响涉及商业、经济、环境、研究、创造绿色就业机会以及屋顶安装和其他大型安装。该项目吸引了公众、投资者和开发商在巴林王国投资类似项目;尤其是它是一种环保和智能的技术。这个创新的智能电网连接的5兆瓦太阳能光伏发电厂足以在10千瓦的功率下为500户房屋供电,并回答了许多令人沮丧的问题,如灰尘对光伏性能的影响、与自然清洁的光伏板相比需要人工清洁、系统的可靠性、温室气体减少和回报期。
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引用次数: 7
Analyzing and Projection of Future Bangladesh Population Using Logistic Growth Model 运用Logistic增长模型分析和预测未来孟加拉国人口
Pub Date : 2019-07-04 DOI: 10.4236/IJMNTA.2019.83004
M. Ullah, G. Mostafa, N. Jahan, Md. Abdul Hakim Khan
Bangladesh is a densely populated country than many other countries of the world. The population growth is termed as alarming, however, knowledge of growth in the years to come would be useful in planning for the development of the country. This article is based on the projection of future population growth of the country. The available actual population census data during 1991-2011 of Bangladesh was applied to the application of a non-linear, non-autonomous ordinary differential equation familiar as Verhulst logistic population model with the maximum environmental capability of Bangladesh. Bangladesh will reach its carrying capacity of 245.09 million population in the next 56 years i.e. the year 2067 and then it decreases as S-shaped curve. The article has provided a focus on the changing trends of the growth of the population of Bangladesh.
孟加拉国是一个比世界上许多其他国家人口稠密的国家。人口增长被称为令人震惊,然而,了解未来几年的增长将有助于规划国家的发展。这篇文章是根据对该国未来人口增长的预测写成的。将孟加拉国1991-2011年的实际人口普查数据应用于孟加拉国最大环境容量的非线性非自治常微分方程Verhulst logistic人口模型。孟加拉国将在未来56年即2067年达到24509万人口的承载能力,然后呈s型曲线下降。这篇文章着重介绍了孟加拉国人口增长的变化趋势。
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引用次数: 4
Analysis of the Precision of Bispectral Estimation Methods 双谱估计方法的精度分析
Pub Date : 2019-07-04 DOI: 10.4236/IJMNTA.2019.83005
Wen-bing Wu
In order to evaluate the accuracy of bispectral estimation method, signals of cosine function were adopted. Because the cosine signals’ three order moment spectrum and three order cumulant spectrum are zero, Non zero part of the bispectrum estimated by no matter which method is the estimation error. Through the comparison of three kinds of estimation methods: the direct method, indirect method and AR parameter method, errors of various estimation methods were obtained, then changing the values of different parameters in all methods, and observing the bispectral error values changes with the parameters, so as to provide a basis for the various bispectrum estimation method and the selection.
为了评估双谱估计方法的准确性,采用了余弦函数信号。由于余弦信号的三阶矩谱和三阶累积量谱为零,因此无论哪种方法估计的双谱的非零部分都是估计误差。通过对直接法、间接法和AR参数法三种估计方法的比较,得出了各种估计方法的误差,然后改变所有方法中不同参数的值,观察双谱误差值随参数的变化,为各种双谱估计方法的选择提供依据。
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引用次数: 0
Existence of Random Attractor Family for a Class of Nonlinear Higher-Order Kirchhoff Equations 一类非线性高阶Kirchhoff方程的随机吸引子族的存在性
Pub Date : 2019-04-23 DOI: 10.4236/IJMNTA.2019.82003
Guoguang Lin, C. Zhu
The existence of random attractor family for a class of nonlinear nonlocal higher-order Kirchhoff partial differential equations with additive white noise is studied. The weak solution of the equation is established by the Ornstein-Uhlenbeck process to deal with the random term, and a bounded random absorption set is obtained. And then, the existence of the random attractor family is proved by the isomorphism mapping method.
研究了一类具有加性白噪声的非线性非局部高阶Kirchhoff偏微分方程的随机吸引子族的存在性。利用Ornstein-Uhlenbeck过程建立了方程的弱解来处理随机项,得到了有界随机吸收集。然后用同构映射方法证明了随机吸引子族的存在性。
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引用次数: 1
Numerical Treatment of Initial Value Problems of Nonlinear Ordinary Differential Equations by Duan-Rach-Wazwaz Modified Adomian Decomposition Method 用改进Adomian分解方法数值处理非线性常微分方程初值问题
Pub Date : 2019-01-31 DOI: 10.4236/IJMNTA.2019.81002
Ö. Umut, Serpil Yaşar
We employ the Duan-Rach-Wazwaz modified Adomian decomposition method for solving initial value problems for the systems of nonlinear ordinary differential equations numerically. In order to confirm practicality, robustness and reliability of the method, we compare the results from the modified Adomian decomposition method with those from the MATHEMATICA solutions and also from the fourth-order Runge Kutta method solutions in some cases. Furthermore, we apply Pade approximants technique to improve the solutions of the modified decomposition method whenever the exact solutions exist.
本文采用改进的Adomian分解方法对非线性常微分方程系统的初值问题进行了数值求解。为了验证该方法的实用性、鲁棒性和可靠性,我们将改进的Adomian分解方法与MATHEMATICA解和四阶Runge Kutta法解的结果进行了比较。此外,在存在精确解的情况下,应用Pade近似技术对改进分解方法的解进行改进。
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引用次数: 2
Bifurcation Analysis of Reduced Network Model of Coupled Gaussian Maps for Associative Memory 联想记忆耦合高斯映射简化网络模型的分岔分析
Pub Date : 2019-01-31 DOI: 10.4236/IJMNTA.2019.81001
Mio Kobayashi, T. Yoshinaga
This paper proposes an associative memory model based on a coupled system of Gaussian maps. A one-dimensional Gaussian map describes a discrete-time dynamical system, and the coupled system of Gaussian maps can generate various phenomena including asymmetric fixed and periodic points. The Gaussian associative memory can effectively recall one of the stored patterns, which were triggered by an input pattern by associating the asymmetric two-periodic points observed in the coupled system with the binary values of output patterns. To investigate the Gaussian associative memory model, we formed its reduced model and analyzed the bifurcation structure. Pseudo-patterns were observed for the proposed model along with other conventional associative memory models, and the obtained patterns were related to the high-order or quasi-periodic points and the chaotic trajectories. In this paper, the structure of the Gaussian associative memory and its reduced models are introduced as well as the results of the bifurcation analysis are presented. Furthermore, the output sequences obtained from simulation of the recalling process are presented. We discuss the mechanism and the characteristics of the Gaussian associative memory based on the results of the analysis and the simulations conducted.
提出了一种基于高斯映射耦合系统的联想记忆模型。一维高斯映射描述了一个离散时间动力系统,高斯映射的耦合系统可以产生不对称的固定点和周期点等各种现象。高斯联想记忆通过将耦合系统中观察到的非对称双周期点与输出模式的二进制值相关联,可以有效地回忆起输入模式触发的存储模式。为了研究高斯联想记忆模型,我们建立了它的简化模型,并对其分岔结构进行了分析。该模型与其他传统的联想记忆模型一起观察到伪模式,所得到的模式与高阶或准周期点和混沌轨迹有关。本文介绍了高斯联想记忆的结构及其简化模型,并给出了分岔分析的结果。在此基础上,给出了回收过程仿真的输出序列。在分析和仿真的基础上,讨论了高斯联想记忆的机理和特点。
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引用次数: 0
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现代非线性理论与应用(英文)
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