scholarly journals Numerical Study on Stochastic Diabetes Mellitus Model with Additive Noise

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Zhifang Zhang ◽  
Qingyi Zhan ◽  
Xiangdong Xie
Keyword(s):  
Diabetes Mellitus ◽  
Existence And Uniqueness ◽  
Additive Noise ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Stability And Convergence ◽  
Mean Square ◽  
Existence And Uniqueness Theorem ◽  
Mean Square Stability ◽  
The Mean

This article focuses on the numerical analysis and simulation of the stochastic diabetes mellitus model with additive noise. The existence and uniqueness theorem of the solution under some appropriate assumptions is established. And, the mean square stability and convergence of numerical solutions are proposed, too. The practical use of these theorems is demonstrated in the numerical computations of the stochastic diabetes mellitus model and the value for the forecast of the tendency of diabetes mellitus in a given time.

scholarly journals A Compensated Numerical Method for Solving Stochastic Differential Equations with Variable Delays and Random Jump Magnitudes

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Ying Du ◽  
Changlin Mei
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Method ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Mean Square ◽  
Variable Delays ◽  
Mean Square Stability ◽  
The Mean ◽  
Random Jump

Stochastic differential equations with jumps are of a wide application area especially in mathematical finance. In general, it is hard to obtain their analytical solutions and the construction of some numerical solutions with good performance is therefore an important task in practice. In this study, a compensated split-stepθmethod is proposed to numerically solve the stochastic differential equations with variable delays and random jump magnitudes. It is proved that the numerical solutions converge to the analytical solutions in mean-square with the approximate rate of 1/2. Furthermore, the mean-square stability of the exact solutions and the numerical solutions are investigated via a linear test equation and the results show that the proposed numerical method shares both the mean-square stability and the so-called A-stability.

scholarly journals Convergence Rate of Numerical Solutions for Nonlinear Stochastic Pantograph Equations with Markovian Switching and Jumps

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Zhenyu Lu ◽  
Tingya Yang ◽  
Yanhan Hu ◽  
Junhao Hu
Keyword(s):  
Brownian Motion ◽  
Convergence Rate ◽  
Existence And Uniqueness ◽  
Numerical Solutions ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Mean Square ◽  
Mean Square Convergence ◽  
The Mean ◽  
Strong Order

The sufficient conditions of existence and uniqueness of the solutions for nonlinear stochastic pantograph equations with Markovian switching and jumps are given. It is proved that Euler-Maruyama scheme for nonlinear stochastic pantograph equations with Markovian switching and Brownian motion is of convergence with strong order 1/2. For nonlinear stochastic pantograph equations with Markovian switching and pure jumps, it is best to use the mean-square convergence, and the order of mean-square convergence is close to 1/2.

Piezoelectric Array Sensing for Real-Time, Broad-Band Sound Radiation Measurement

1999 ◽  
Vol 121 (4) ◽  
pp. 446-452 ◽  
Author(s):  
A. Preumont ◽  
A. Franc¸ois ◽  
S. Dubru
Keyword(s):  
Numerical Study ◽  
Broad Band ◽  
Sound Radiation ◽  
Radiation Measurement ◽  
Mean Square ◽  
Noise Radiation ◽  
Radiation Sensor ◽  
Reconstructed Volume ◽  
The Mean ◽  
Array Sensing

This paper proposes a noise radiation sensor consisting of an array of independent piezoelectric patches connected to an adaptive linear combiner. The coefficients of the linear combiner are adapted in such a way that the mean-square error between the reconstructed volume displacement (or velocity) and either numerical or experimental data is minimized. A numerical study is conducted, to analyze the influence of the size of the piezoelectric array on the reconstructed volume velocity.

scholarly journals Stability of Analytical and Numerical Solutions for Nonlinear Stochastic Delay Differential Equations with Jumps

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Qiyong Li ◽  
Siqing Gan
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Numerical Solutions ◽  
Mean Square ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Analytical And Numerical Solutions ◽  
Mean Square Stability ◽  
Delay Differential

This paper is concerned with the stability of analytical and numerical solutions fornonlinearstochastic delay differential equations (SDDEs) with jumps. A sufficient condition for mean-square exponential stability of the exact solution is derived. Then, mean-square stability of the numerical solution is investigated. It is shown that the compensated stochastic θ methods inherit stability property of the exact solution. More precisely, the methods are mean-square stable for any stepsizeΔt=τ/mwhen1/2≤θ≤1, and they are exponentially mean-square stable if the stepsizeΔt∈(0,Δt0)when0≤θ<1. Finally, some numerical experiments are given to illustrate the theoretical results.

scholarly journals Statistical-mechanical analysis of adaptive filter with clipping saturation-type nonlinearity

2021 ◽  
Author(s):  
Seiji Miyoshi
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Asymptotic Analysis ◽  
Adaptive Filter ◽  
Adaptive System ◽  
Adaptive Signal Processing ◽  
Mean Square ◽  
Mean Square Stability ◽  
Statistical Mechanical ◽  
The Mean

Adaptive signal processing is used in broad areas. In most practical adaptive systems, there exists substantial nonlinearity that cannot be neglected. In this paper, we analyze the behaviors of an adaptive system in which the output of the adaptive filter has the clipping saturation-type nonlinearity by a statistical-mechanical method. To represent the macroscopic state of the system, we introduce two macroscopic variables. By considering the limit in which the number of taps of the unknown system and adaptive filter is large, we derive the simultaneous differential equations that describe the system behaviors in the deterministic and closed form. Although the derived simultaneous differential equations cannot be analytically solved, we discuss the dynamical behaviors and steady state of the adaptive system by asymptotic analysis, steady-state analysis, and numerical calculation. As a result, it becomes clear that the saturation value S has the critical value SC at which the mean-square stability of the adaptive system is lost. That is, when S > SC, both the mean-square error (MSE) and mean-square deviation (MSD) converge, i.e., the adaptive system is mean-square stable. On the other hand, when S < SC, the MSD diverges although the MSE converges, i.e., the adaptive system is not mean-square stable. In the latter case, the converged value of the MSE is a quadratic function of S and does not depend on the step size. Finally, SC is exactly derived by asymptotic analysis.<br>

scholarly journals A Comparison Theorem for Stability of Linear Stochastic Implicit Difference Equations of Index-1

2020 ◽  
Vol 36 (3) ◽  
Author(s):  
Nguyen Hong Son
Keyword(s):  
Comparison Theorem ◽  
Difference Equations ◽  
Mean Square ◽  
Mean Square Stability ◽  
Method Of Solution ◽  
The Mean ◽  
Definition Of

In this paper we study linear stochastic implicit difference equations (LSIDEs for short) of index-1. We give a definition of solution and introduce an index-1 concept for these equations. The mean square stability of LSIDEs is studied by using the method of solution evaluation. An example is given to illustrate the obtained results.

Cooperative guidance law considering the randomness of the unreliable communication network

2018 ◽  
Vol 233 (9) ◽  
pp. 3313-3322
Author(s):  
Chunyan Zhang ◽  
Jianmei Song ◽  
Lan Huang ◽  
Gaohua Cai
Keyword(s):  
Communication Network ◽  
Consensus Algorithm ◽  
Mean Square ◽  
Cooperative System ◽  
Proportional Navigation ◽  
Impact Time ◽  
Guidance Law ◽  
Mean Square Stability ◽  
Cooperative Guidance ◽  
The Mean

The cooperative attack problem of multiple missiles considering the randomness of the unreliable communication network is investigated. Firstly, the stochastic communication network is described by a Bernoulli random model. And the cooperative guidance law with unreliable communication network is proposed, which is composed of the upper consensus algorithm of desired impact time and the local proportional navigation with time-varying navigation gain. Each node of the upper cooperative system uses different update gain to adjust the desired impact time to improve the cooperative performance. Secondly, the mean square stability of the upper cooperative system is analyzed and proved. The explicit necessary and sufficient conditions of the mean square stability are presented for the two-missile cooperative attack system. And the analytic expression of the mean of the cooperative impact time is derived since it influences the attack precision directly and significantly. Thirdly, the effectiveness of the proposed cooperative guidance law with unreliable communication network is verified by simulation. And the influence of the update gain, the communication step, and the mean of link probability on the cooperative attack precision is analyzed.

Sign in / Sign up

Export Citation Format

Share Document