一类基于比率且具双线性密度制约的捕食-食饵系统的全局稳定性分析

研究一类基于比率和具双线性密度制约的捕食-食饵系统．由Bendixson环域定理及比较定理给出了奇点（0,0）和（1,0）全局渐近稳定的条件．通过对等倾线的研究给出了正平衡点存在的条件,并构造了Dulac函数讨论其全局渐近稳定性．     

具有leakage时滞与随机干扰的离散神经网络渐近稳定性分析

研究了一类具有leakage时滞与随机干扰的离散型神经网络的全局渐近稳定性问题．利用一种新的时滞分割方法将时滞区间分割为多个区间．通过构造新的Lyapunov泛函得到了基于线性矩阵不等式（LMI）的渐近稳定性判据．该判据在获得更小的保守性同时也降低了计算的复杂度．     

多时滞三种群捕食模型的持久性和全局渐近性

研究了一类多时滞非自治三种群捕食模型的持久性和全局渐近稳定性,分别利用比较原理和构造Lyapunov函数方法得到了模型持久生存与全局渐近稳定性的充分条件,并举例说明定理的可行性且利用Matlab绘出图像.     

潜伏期具有传染性的SEIRS流行病模型的全局稳定性

研究一类潜伏期和染病期均具有传染性和康复可能的SEIRS流行病模型,确定了疾病流行与否的阈值,利用Routh-Hurwitz判据和LaSalle不变集原理得到无病平衡点的全局渐近稳定性,并借助广义Bendixson-Dulac定理得到地方病平衡点的全局渐近稳定性,最后给出数值模拟.     

一类具有反馈控制的随机SI传染病模型的全局稳定性（英文）

文章首次提出了一类具有反馈控制的随机SI传染病模型,得到了随机系统全局渐近稳定性的充分条件.结论是如果确定系统的地方病平衡点是全局稳定的,那么只要扰动充分小,其相应的随机系统也是全局稳定的.最后进行了数值模拟,验证了理论结果的有效性.     

具有比率依赖型功能反应函数的食饵-捕食者征税模型分析

本文研究了一个具有功能反应函数的食饵一捕食者征税模型,得到了该系统正平衡点的存在性、局部渐近稳定性和全局渐近稳定性的条件,并利用Pontrjagin最大值原理得到了最优税收策略．该文为资源管理者制定合理的管理政策提供理论依据．     

一类食饵具有S-型变收获率的非自治离散捕食系统渐近行为

建立并研究了一类具有S-型变收获率的非自治离散捕食系统,应用差分不等式、Brouwer不动点定理和分析技巧分别建立了系统的持久生存性,正周期解的存在性及全局渐近稳定性的充分条件,我们还给出了具体验证例子及相应的数值模拟结果.     

具有庇护所的三种群捕食者-食饵模型

讨论了一类具有庇护所的自治三种群捕食者一食饵模型,运用Liapunov函数方法,得到了该模型持久性的充分条件．对于该模型的周期系统,在一定的条件下,将产生唯一一个全局渐近稳定的周期正解．对更具普遍意义的概周期现象,也得出了概周期正解唯一存在且全局渐近稳定性的充分条件．     

具有脉冲和时滞的Lotka-Volterra系统的正周期解的存在性和全局渐近稳定性

主要研究具有脉冲和时滞的Lotka-Volterra系统的正周期解的存在性和全局渐近稳定性．     

一个有相互干扰的食植系统的研究

本文运用常微分方程定性理论讨论了一个放牧有相互干扰的食植系统,获得了该系统极限环存在唯一性及全局渐近稳定性的充分条件．     

Blowing-up of deterministic fixed points in stochastic population dynamics

We discuss the stochastic dynamics of biological (and other) populations presenting a limit behaviour for large environments (called deterministic limit) and its relation with the dynamics in the limit. The discussion is circumscribed to linearly stable fixed points of the deterministic dynamics, and it is shown that the cases of extinction and non-extinction equilibriums present different features. Mainly, non-extinction equilibria have associated a region of stochastic instability surrounded by a region of stochastic stability. The instability region does not exist in the case of extinction fixed points, and a linear Lyapunov function can be associated with them. Stochastically sustained oscillations of two subpopulations are also discussed in the case of complex eigenvalues of the stability matrix of the deterministic system.     

Stochastic instability and Liapunov stability

Summary The relationship between the deterministic stability of nonlinear ecological models and the properties of the stochastic model obtained by adding weak random perturbations is studied. It is shown that the expected escape time for the stochastic model from a bounded region with nonsingular boundary is determined by a Liapunov function for the nonlinear deterministic model. This connection between stochastic and deterministic models brings together various notions of persistence and vulnerability of ecosystems as defined for deterministically perturbed or randomly perturbed models.     

One- and multi-locus multi-allele selection models in a random environment

Summary We deduce conditions for stochastic local stability of general perturbed linear stochastic difference equations widely applicable in population genetics. The findings are adapted to evaluate the stability properties of equilibria in classical one- and multi-locus multi-allele selection models influenced by random temporal variation in selection intensities. As an example of some conclusions and biological interpretations we analyse a special one-locus multi-allele model in more detail.This work was supported in part by Stiftung Volkswagenwerk.     

Steady states in population models with monotone,stochastic dynamics

Existence, uniqueness and asymptotic stability of stochastic equilibrium are established in multi-dimensional population models with monotone dynamics.     

Exploring the implicit interlayer regulatory mechanism between cells and tissue: Stochastic mathematical analyses of the spontaneous ordering in beating synchronization

The present study focused on beating synchronization, and tried to elucidate the interlayer regulatory mechanisms between the cells and clump in beating synchronization with using the stochastic simulations which realize the beating synchronizations in beating cells with low cell–cell conductance. Firstly, the fluctuation in interbeat intervals (IBIs) of beating cells encouraged the process of beating synchronization, which was identified as the stochastic resonance. Secondly, fluctuation in the synchronized IBIs of a clump decreased as the number of beating cells increased. The decrease in IBI fluctuation due to clump formation implied both a decline of the electrophysiological plasticity of each beating cell and an enhancement of the electrophysiological stability of the clump. These findings were identified as the community effects. Because IBI fluctuation and the community effect facilitated the beating stability of the cell and clump, these factors contributed to the spontaneous ordering in beating synchronization. Thirdly, the cellular layouts in clump affected the synchronized beating rhythms. The synchronized beating rhythm in clump was implicitly regulated by a complicated synergistic effect among IBI fluctuation of each beating cell, the community effect and the cellular layout. This finding was indispensable for leading an elucidation of mechanism of emergence. The stochastic simulations showed the necessity of considering the synergistic effect, to elucidate the interlayer regulatory mechanisms in biological system.     

Role of gestation delay in a plankton-fish model under stochastic fluctuations

The present paper studies a minimal prey-predator model in the context of marine plankton interaction together with predation by planktivorous fish. The time lag required for gestation of the predator is incorporated and the resulting delayed model is analyzed for stability and bifurcation phenomena. A stochastic extension of the model is considered by perturbing the growth process of phytoplankton using colored noise process known to be more appropriate for the marine environment. The stochastic models with and without gestation delay are analyzed for stability aspects and a threshold value of gestation delay is obtained; this threshold is then compared with that of the deterministic model.     

The stabilizing effect of a random environment

It is shown that the lottery competition model permits coexistence in a stochastic environment, but not in a constant environment. Conditions for coexistence and competitive exclusion are determined. Analysis of these conditions shows that the essential requirements for coexistence are overlapping generations and fluctuating birth rates which ensure that each species has periods when it is increasing. It is found that a species may persist provided only that it is favored sufficiently by the environment during favorable periods independently of the extent to which the other species is favored during its favorable periods.Coexistence is defined in terms of the stochastic boundedness criterion for species persistence. Using the lottery model as an example this criterion is justified and compared with other persistence criteria. Properties of the stationary distribution of population density are determined for an interesting limiting case of the lottery model and these are related to stochastic boundedness. An attempt is then made to relate stochastic boundedness for infinite population models to the behavior of finite population models.     

Alternative (un)stable states in a stochastic predator–prey model

Stochastic models sometimes behave qualitatively differently from their deterministic analogues. We explore the implications of this in ecosystems that shift suddenly from one state to another. This phenomenon is usually studied through deterministic models with multiple stable equilibria under a single set of conditions, with stability defined through linear stability analysis. However, in stochastic systems, some unstable states can trap stochastic dynamics for long intervals, essentially masquerading as additional stable states. Using a predator–prey model, we demonstrate that this effect is sufficient to make a stochastic system with one stable state exhibit the same characteristics as an analogous system with alternative stable states. Although this result is surprising with respect to how stability is defined by standard analyses, we show that it is well-anticipated by an alternative approach based on the system's “quasi-potential.” Broadly, understanding the risk of sudden state shifts will require a more holistic understanding of stability in stochastic systems.     

Robust filtering for stochastic genetic regulatory networks with time-varying delay

This paper addresses the robust filtering problem for a class of linear genetic regulatory networks (GRNs) with stochastic disturbances, parameter uncertainties and time delays. The parameter uncertainties are assumed to reside in a polytopic region, the stochastic disturbance is state-dependent described by a scalar Brownian motion, and the time-varying delays enter into both the translation process and the feedback regulation process. We aim to estimate the true concentrations of mRNA and protein by designing a linear filter such that, for all admissible time delays, stochastic disturbances as well as polytopic uncertainties, the augmented state estimation dynamics is exponentially mean square stable with an expected decay rate. A delay-dependent linear matrix inequality (LMI) approach is first developed to derive sufficient conditions that guarantee the exponential stability of the augmented dynamics, and then the filter gains are parameterized in terms of the solution to a set of LMIs. Note that LMIs can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures.