与年龄相关的模糊随机种群扩散系统的指数稳定性

讨论了一类与年龄相关的模糊随机种群扩散系统,系统受两种不确定性因素的影响,即随机和模糊.在有界和Lipschitz条件下,利用Ito公式和Gronwall引理,建立了均方意义下与年龄相关的模糊随机种群扩散系统指数稳定性的判定准则并通过数值例子对所给出的结论进行了验证.     

与年龄相关的模糊随机种群扩散系统的数值解

讨论了一类与年龄相关的模糊随机种群扩散系统的数值解。系统同时受两种不确定性因素的影响。即,随机和模糊。并根据Euler-Maruyama方法给出了模糊随机种群扩散系统的数值解表达式,在有界的条件(弱于线性增长条件)和Lipschitz条件下,证明了方程的数值解在均方意义下收敛于解析解。通过例子对本文的算法进行了验证。     

与年龄相关的模糊随机种群系统的半隐式Euler法的收敛性

介绍了一类与年龄相关的模糊随机种群系统的半隐式Euler法.系统同时受到两种不确定性因素的影响:即,随机和模糊.在有界的条件(弱于线性增长条件)和Lipschitz条件下,讨论了与年龄相关的模糊随机种群系统在半隐式Euler法下的收敛性.方法具有克服线性计算不稳定的优点.最后通过例子对算法进行了验证.     

环境污染下与年龄相关模糊随机种群系统的指数稳定性

讨论了一类在环境污染下与年龄相关的模糊随机种群系统,该系统不仅考虑了环境污染、外界环境噪声对种群的影响,而且设初值是一个模糊数.在有界和Lipschitz条件下,运用Ito公式和Gronwall引理,给出了环境污染下与年龄相关模糊随机种群系统指数稳定性的判定准则.并通过数值算例对所给结论进行了验证.     

与年龄相关的随机时滞种群方程的指数稳定性

本文研究了与年龄相关的随机时滞种群方程,运用Burkholder-Davis-Gundy定理和改进的coercivity条件,建立了均方意义和几乎处处意义下与年龄相关的随机时滞种群方程稳定性的判定准则,得到了保证强解稳定的若干充分条件.     

与年龄相关的随机时滞种群方程的指数稳定性

本文研究了与年龄相关的随机时滞种群方程,运用Burkholder-Davis-Gundy定理和改进的 coercivity条件,建立了均方意义和几乎处处意义下与年龄相关的随机时滞种群方程稳定性的判定准则,得到了保证强解稳定的若干充分条件．     

带Poisson跳年龄相关随机时滞种群系统的均方稳定性

本文研究了带Poisson跳年龄相关随机时滞种群系统均方稳定性的问题.在一定条件下,给出了数值解均方稳定的定义.利用补偿随机θ法讨论系统数值解的均方稳定性,给出数值解稳定的充分条件.获得了当1/2≤θ≤1时,对于任意的步长?τ/m,数值解是均方稳定的;当0≤θ1,时,如果步长?t∈(0,?t0),数值解是指数均方稳定的的结果.最后通过数值算例推广并验证了结果的有效性和正确性.     

带跳和分数Brown运动的固定资产系统倒向Euler数值解的均方渐近有界性

介绍了一类与年龄相关的随机固定资产系统倒向Euler数值解法.漂移系数和扩散系数在单边Lipschitz条件和有界条件下,建立了随机固定资产系统倒向Euler数值解均方渐近有界性的判定准则.最后通过数值算例对结论进行了验证.     

具有年龄和加权的非线性随机种群系统的最优边界控制

讨论了与年龄相关的非线性随机种群系统的最优边界控制问题,在外界环境对种群系统产生影响的条件下,考虑了种群的加权系数,应用积分-偏微分方程和变分不等式导出控制为最优的必要条件,得到最优性组.     

分数阶与年龄相关的随机种群系统的逼近控制

讨论了一类分数阶与年龄相关的随机种群系统的逼近控制.通过不动点原理,分数阶性质和随机微分方程基本理论,建立了分数阶与年龄相关的随机种群控制系统弱解存在的必要条件,并给出了该系统逼近控制的条件,最后通过数值例子对所给出的结论进行了验证.     

Exponential stability of numerical solutions to a stochastic age-structured population system with diffusion

The main aim of this paper is to investigate the exponential stability of the Euler method for a stochastic age-structured population system with diffusion. The definition of exponential mean square stability of numerical method is introduced. It is proved that the Euler scheme is exponentially stable in mean square sense. An example is given for illustration.     

Banach空间中带Poisson跳的随机种群方程的数值分析

本文研究Banach空间中带Poisson跳的随机种群方程,通过离散使之成为随机微分方程,进而运用显式Euler公式来分析其数值解与解析解的误差.     

Convergence of numerical solutions to stochastic age-structured system of three species

In general, most of stochastic age-structured system of three species do not have explicit solutions, thus numerical approximation schemes are invaluable tools for exploring their properties. The aim of this paper is to investigate the convergence of numerical approximation solution to the true solution for stochastic age-structured system of three species.     

Mathematical modeling of the receptor-mediated endocytosis process of targeted therapeutic agents in drug delivery systems

In this paper, we propose mathematical models to describe receptor-mediated endocytosis processes. One is a stochastic differential model for the agent-target binding process. The mean extinction time and a standard variation over time profile are evaluated. The other is an age-structured model for demonstrating endocytosis and lysosome processes. A targeted drug delivery system has a complex process in how it is to deliver drug molecules in terms of administration, transportation in blood and across membranes to intracellular space, and inhibition to microtubule polymerization. In particular, receptor-mediated endocytosis of targeted therapeutic agents, such as antibody drug conjugates or ligand-targeted liposome encapsulated nanoparticles, is a key step in understanding the drug delivery mechanism. We discuss stochastic quasi steady state approximation when agent-target complex does not appreciably vary compared with the free agents. This reduces the number of the systems and the parameters; however, an initial time phase cannot be captured. In addition, we discuss the strengths and weaknesses when the age-structured model induces the reduced model compared with the full model that considers endocytosis and lysosome processes. If the total mean retention time until payload release in intracellular space is known, then the age-structured model with the Erlang distribution may fairly predict data of the released payload over time profile with far fewer parameters; however, induced compartments lose their physical meaning and describe only a delay.     

具扩散的年龄结构脉冲随机时滞种群方程的均方稳定性(英文)

本文考虑一类具扩散的年龄结构脉冲随机时滞种群方程.主要目的是研究具扩散的年龄结构脉冲随机时滞种群平凡解的均方稳定性,给定两个使平凡解均方稳定的充分条件.     

Numerical approximation of a stochastic age-structured population model in a polluted environment with Markovian switching

In this paper, a stochastic age-structured population model with Markovian switching is investigated in a polluted environment. Both the stochastic disturbance of environment and the Markovian switching are incorporated into the model. By Itô formula and several assumptions, the boundedness in the qth moment of exact solutions of model are proved. Furthermore, making use of truncated Euler–Maruyama (EM) method, the strong convergence criterion of numerical approximation in the qth moment is established, and the rate of convergence is estimated. Numerical simulations are carried out to illustrate the theoretical results. Our results indicate that the truncated EM method can be used for stochastic age-structured population system in a polluted environment.     

New robust passivity criteria for stochastic fuzzy BAM neural networks with time-varying delays

In this paper, we consider the problem of passivity analysis issue for a class of stochastic fuzzy BAM neural networks with time varying delays. By employing the idea of delay-fractioning technique and Lyapunov stability theory, a new set of sufficient conditions are derived in terms of linear matrix inequalities for obtaining the passivity condition of the considered neural network model. First, we derive the passivity condition for stochastic fuzzy BAM neural networks with time varying delays and then the result is extended to the case with uncertainties. Two numerical examples are given to illustrate the effectiveness and conservatism of the obtained results.     

Global asymptotic stability for an age-structured model of hematopoietic stem cell dynamics

We investigate a system of two nonlinear age-structured partial differential equations describing the dynamics of proliferating and quiescent hematopoietic stem cell (HSC) populations. The method of characteristics reduces the age-structured model to a system of coupled delay differential and renewal difference equations with continuous time and distributed delay. By constructing a Lyapunov–Krasovskii functional, we give a necessary and sufficient condition for the global asymptotic stability of the trivial steady state, which describes the population dying out. We also give sufficient conditions for the existence of unbounded solutions, which describe the uncontrolled proliferation of HSC population. This study may be helpful in understanding the behavior of hematopoietic cells in some hematological disorders.     

Coexistence steady states in a predator–prey model

An age-structured predator–prey system with diffusion and Holling–Tanner-type nonlinearities is investigated. Regarding the intensity of the fertility of the predator as bifurcation parameter, we prove that a branch of positive coexistence steady states bifurcates from the marginal steady state with no predator. A similar result is shown when the fertility of the prey varies.