共查询到19条相似文献，搜索用时 648 毫秒
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为了研究核转录因子kappa B（NF-κB）信号转导网络的内部结构和相互关联的参数对系统输出信号的影响，进行参数敏感性分析和系统模型简化是十分必要的。通过对基于TNF-α诱导的NF-κB信号转导网络数学模型进行分析，选择IKK作为系统的阶跃输入信号和NF-κBn作为系统的可测输出，利用直接微分法分析振荡输出信号NF-κBn关于64个模型参数的敏感性，并选择适当的允许误差目标函数ε，将原系统模型中的9个不敏感参数删除进行模型化简。仿真结果表明，原模型与简化模型的系统输出NF-κBn完全吻合，同时，简化模型的其余25个状态输出也与原模型的输出基本一致。因此，参数敏感性分析和模型简化结果为生物数据分析，模型建立和实验设计提供了有益的参考价值。 相似文献
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随着计算机迅速发展,利用计算机来进行仿真分析时可以求解一些无法利用理论分析解答的问题,待分析的实际问题多为三维图形,但利用分析软件对三维模型进行分析时,所需的计算量非常大,大多数情况下是将形状规则的三维模型简化为二维模型,但简化是有一定条件的,以电容器为例,利用ANSYS分析软件分析了阴极有圆锥型突起时的电场分布,与二维简化的模型进行了计算对比,从而得出简化模型的局限性。 相似文献
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[研究目的]在网络舆情从定性研究向定量研究的过渡过程中,精细化的数学建模对于揭示舆情传播规律、舆情趋势预测以及舆情科学管控等问题都具有重要的理论与实际意义。[研究方法]分数阶微积分学框架下,针对网络舆情系统构建可充分融和历史信息影响因素的分数阶微分方程模型,并借助分数阶导数的定义给出数学模型参数拟合方法,进而实现网络舆情系统更为精细的数学建模。[研究结论]以一类实际网络舆情事件为范例,通过分数阶数学模型的建立与基于数据的模型参数拟合,展示了基于分数阶微分方程建模方法的先进性与准确性,进一步降低了网络舆情系统整数阶数学建模方法的保守性。 相似文献
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数学建模是利用数学方法解决实际问题的一种实践。即通过抽象、简化、假设、引进变量等处理过程后,将实际问题用数学方式表达,建立起数学模型,然后运用先进的数学方法及计算机技术进行求解。数学建模将各种知识综合应用于解决实际问题中,是培养和提高学生应用所学知识分析问题、解决问题的能力的必备手段之一。本文通过建立微分方程模型利用常微分方程知识进行定量或定性的分析,找到规律、了解事物本质,看常微分方程在现实中的应用。 相似文献
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本文用基于无源的方法对球杆系统进行动能和势能的修订来镇定系统,通过互联和阻尼配置的技术将系统的偏微分方程简化为简单的非线性常微分方程,就可以得到一个渐近稳定的控制器. 相似文献
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基于Flowmaster的燃油系统模型简化方法 总被引：1，自引：0，他引：1
通过建立某轻型水陆两栖飞机燃油系统Flowmaster仿真计算模型,对不同简化条件下仿真计算结果与试验结果之间的差异进行了对比,提出了燃油系统常用部件模型简化的基本方法。 相似文献
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以非线性波动微分方程作为研究对象,运用李群分支算法对其进行变量分离及精确解分析。首先,利用不变子空间法通过线性常微分方程存在解的子空间中构建适合非线性波动微分方程和方程组的不变子空间,将子空间应用至方程算子中并进行降价和化简处理,推导出不变子空间的未知函数,从而得到等价转换的简化方程;其次,采用李群分支法将扩散方程的解空间分划为多个小轨道,选取相应无线维对称群的分支,每个解空间由自同构系统决定,获取方程解需选择对称群并由其构造新方程,再将符号不变量运用至方程组中,使它成为初始给定方程的求解条件,进而实现非线性波动微分方程的变量分离,求出其精确解。实验证明,所提方法可实现变量分离,得到精确解,为当代数学提供理论支持。 相似文献
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研究采用Bcklund变换的双线性化常微分方程非凸松弛解分析问题,双线性化常微分方程非凸松弛解是保证模型平稳分布和存在性的重要因素,从而提高许多模型在不同边界条件下的稳定特性。把双线性化常微分方程的非凸松弛解算子进行敏感域分析表征,采用Bcklund变换进行目标函数统一迭代,得到非凸松弛解的3种核函数分别是线性核函数、多项式核函数和高斯核函数。计算双线性化常微分方程的非凸松弛解的对称广义中心的稳定性平衡点,计算线性化常微分方程的非凸松弛解满足的边界条件,通过Bcklund变换扩展欧几里得算法,实现对非凸松弛解的稳定性和收敛性的证明,得到在不同多向增量式和减量式分析下,采用Bcklund变换的双线性化常微分方程非凸松弛解是收敛和稳定的。 相似文献
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《Journal of The Franklin Institute》2019,356(5):2901-2918
In this paper, we present a new method in the reduction of large-scale linear differential-algebraic equation (DAE) systems. The approach is to first change the DAE system into a parametric ordinary differential equation (ODE) system via the ε-embedding technique. Next, based on parametric moment matching, we give the parameterized model order reduction (MOR) method to reduce this parametric system, and a new Arnoldi parameterized method is proposed to construct the column-orthonormal matrix. From the reduced-order parametric system, we get the reduced-order DAE system, which can preserve the structure of the original DAE system. Besides, the parametric moment matching for the reduced-order parametric systems is analyzed. Finally, the effectiveness of our method is successfully illustrated via two numerical examples. 相似文献
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A method of analyzing and interpreting trajectory errors in the numerical solution of ordinary differential equations by digital computers is discussed. Truncation in integrating a set of differential equations leads to errors in the trajectory of the solution. An explanation is given for the use of diagrams in the complex plane to evaluate errors in the trajectory, with a discussion of the properties of a number of frequently used integration formulas via the diagrams. The diagrams portray the characteristics of an integration method in more detail than do the absolutely stable regions presented by Dahlquist. Based on the diagrams, guidelines are listed as to how to choose a proper integration formula for the given set of differential equations. A method is presented to check whether or not the numerical solution is satisfactory. 相似文献
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The problem of reduced-order modelling is considered in connection with the design of restricted complexity controllers. The suggested reduction method develops in two phases: (i) a simple frequency response of the overall feedback control system is determined according to the design specifications; (ii) a reduced-order transference of the controlled plant is obtained by solving a linear set of equations in such a way that its behaviour approximates that of the original plant at frequencies which are meaningful for the overall transfer function derived in the first step (e.g. resonance and cutoff frequencies). An example shows how the procedure yields a reduced-order model suitable for designing robust controllers whereas other standard methods, based on properties of the plant only, fail. 相似文献
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The steady two-dimensional stagnation point flow toward a stretching/shrinking sheet with the bottom surface of the sheet heated by convection from a hot fluid is considered. The governing partial differential equations are transformed into ordinary differential equations, before being solved numerically. Results for the skin friction coefficient and the local Nusselt number as well as the temperature profiles are presented for different values of the governing parameters. Effects of the governing parameters on the heat transfer characteristics are thoroughly examined. Different from a stretching sheet, it is found that the solutions for a shrinking sheet are non-unique. 相似文献
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Numerical integration is the most common and straightforward approach in computational neuroscience for the study of biological neuron models based on ordinary differential equations. For some purposes, numerical simulations are not enough due to the multiple bottlenecks in computer architectures. However, when electronic circuits are used to simulate in real time large arrays of coupled neurons, the simulations are much faster than the computer simulations. We present here an electronic implementation of a map-based neuron model, a chaotic Rulkov neuron model, that can be easily transferred on a large scale integration circuit and thus provide a framework for the simulation of large networks of neurons. The Rulkov model is a map-based neuron model that has a surprising abundance of features, such as periodic and chaotic spiking and bursting. The discrete time dynamics allows to tune the time scale of the circuit to the needs of the specific application. Since the circuit described here only uses 18 MOS transistors, it offers new perspectives for building large networks of neurons in a single device. This is very relevant for the analysis of large networks of coupled neurons in order to investigate its dynamics over the network and its synchronization properties. 相似文献
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In this paper, on the basis of the theories and methods of ecology and ordinary differential equation, an ecological model consisting of two preys and one predator with impulsive control strategy and seasonal effects is established. Conditions which guarantee the global asymptotical stability of the prey-eradication periodic solution are obtained using the theory of impulsive equations, small amplitude perturbation skills, and comparison techniques. Further, the influences of the impulsive perturbation and seasonal effects on the inherent oscillation are studied numerically. These show to be consistent with the theoretical analysis and rich complex population dynamics, such as species extinction and permanence. Moreover, the population dynamical behavior of the model is demonstrated by the computed largest Lyapunov exponent. By investigating the strange attractors through their computed Fourier spectra, we know that seasonality has a profound effect on the population dynamical behavior. All these results are expected to be of use in the study of dynamic complexity of ecosystems. 相似文献
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This paper introduces an alternative method artificial neural networks (ANN) used to obtain numerical solutions of mathematical models of dynamic systems, represented by ordinary differential equations (ODEs) and partial differential equations (PDEs). The proposed trial solution of differential equations (DEs) consists of two parts: The initial and boundary conditions (BCs) should be satisfied by the first part. However, the second part is not affected from initial and BCs, but it only tries to satisfy DE. This part involves a feedforward ANN containing adjustable parameters (weight and bias). The proposed solution satisfying boundary and initial condition uses a feedforward ANN with one hidden layer varying the neuron number in the hidden layer according to complexity of the considered problem. The ANN having appropriate architecture has been trained with backpropagation algorithm using an adaptive learning rate to satisfy DE. Moreover, we have, first, developed the general formula for the numerical solutions of nth-order initial-value problems by using ANN.For numerical applications, the ODEs that are the mathematical models of linear and non-linear mass-damper-spring systems and the second- and fourth-order PDEs that are the mathematical models of the control of longitudinal vibrations of rods and lateral vibrations of beams have been considered. Finally, the responses of the controlled and non-controlled systems have been obtained. The obtained results have been graphically presented and some conclusion remarks are given. 相似文献
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In this paper, moment matching model reduction problem for negative imaginary systems is considered. For a given negative imaginary system with poles at the origin, our goal is to find a reduced-order negative imaginary system such that a prescribed number of the moments and the poles at the origin are preserved. Firstly, the original negative imaginary system is split into an asymptotically stable subsystem, a lossless negative imaginary subsystem and an average subsystem. Then, moment matching model reduction is implemented on the asymptotically stable subsystem and the lossless negative imaginary subsystem. The resulting reduced-order system preserves the negative imaginary structure and the poles at the origin. Also, the proposed model reduction method is extended to the positive real systems. Numerical examples demonstrate the effectiveness of the proposed model reduction method. 相似文献
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《Journal of The Franklin Institute》2023,360(7):4519-4547
To ensure better performance and simultaneously save resources, an event-triggered adaptive command filtered dynamic surface control (ACFDSC) method for uncertain stochastic nonstrict-feedback nonlinear systems with dynamic output constraints and prescribed performance is designed in this article. Firstly, with the help of reduced-order K-filters, linearly parameterized neural networks and specific coordinate transformation technique, the unmeasurable states, nonlinearities, two types of unmodeled dynamics and output constraints are dealt with respectively. Then, an event-triggered ACFDSC strategy is proposed to ensure that the tracking error reaches a specific bound within a finite time. By introducing the compensated signal into the complete Lyapunov function, and with the assistance of the compact set defined in the stability analysis, all signals are strictly demonstrated to be semi-globally uniformly ultimately bounded. The simulation results verify the effectiveness of the proposed method. 相似文献