具收获与脉冲的时滞捕食模型研究

研究了与生物资源管理相关的食饵具脉冲扰动与成年捕食者具连续收获的阶段结构时滞捕食-食饵模型.利用离散动力系统的频闪映射和脉冲时滞微分方程理论,得到了捕食者灭绝周期解的全局吸引和系统持久的充分条件,也证明了系统的所有解的一致完全有界.结论为现实的可再生生物资源管理提供了可靠的策略依据.     

一类具有阶段结构和脉冲效应的捕食者-食饵模型的动力学分析

研究了一个捕食者具有阶段结构,食饵具有脉冲效应和时滞的捕食者-食饵模型.利用离散动力系统的频闪映射,我们获得了捕食者-灭绝的周期解同时给出了该周期解全局吸引的充分条件.利用时滞脉冲微分方程的理论,得到了系统持续生存的充分条件.     

具有脉冲时滞效应两食饵-捕食者Watt型功能反应系统分析

这篇文章应用系统生态数学研究了具有脉冲时滞效应两食饵一捕食者Watt型功能反应的模型.通过应用脉冲方程理论,脉冲比较原理以及一些条件得到了捕食者灭绝周期解存在和全局吸引.然后证明了周期解的持久性而且在该条件下系统至少有一个周期解.     

带有年龄结构的捕食者-食饵模型研究

研究带有年龄结构的捕食者-食饵模型的渐近行为.本文所研究的模型假定捕食者从幼年阶段到成年阶段的转变率依赖于幼年种群的密度,还假定幼年捕食者捕食食饵.本文最终给出了有年龄结构的捕食者-食饵模型的捕食者持久和灭绝的若干条件.     

在脉冲污染环境中具有阶段结构的捕食食饵Gompertz模型的动力学性质

研究了在脉冲污染环境中,捕食者具有阶段结构的捕食食饵Gompertz模型的动力学性质,获得了捕食者灭绝周期解全局吸引和系统持续生存的条件.     

一类食饵具有常数收获率和Holling Ⅲ型功能性反应的捕食者-食饵模型的定性分析

本文对捕食者种群、食饵种群均在线性密度制约的条件下,食饵种群具有常数收获率的HollingⅢ型功能性反应模型进行定性分析,通过运用定性分析的方法和利用Dulac函数方法,分别讨论了模型正平衡点稳定性、极限环的存在性以及无穷远奇点的稳定性,得到了正平衡点存在的条件和在其周围不存在极限环的条件,以及无穷远点的性态,并给出了模型轨线的全局结构图.最后,对该模型作了数值的仿真模拟验证.     

具有时滞的三种群随机捕食-食饵模型

本文研究一个具有时滞三种群随机捕食-食饵模型;首先,确定系统对正的初始条件存在唯一的全局正解,其次,证明了系统均值有界且获得了种群灭绝与平均持续生存的条件.     

一类带一般功能反应的病原体捕食者-食饵模型中避难所的影响

本文讨论一类SIP型捕食者-食饵-病原体扩散模型,其中捕食者带有一般的功能反应函数.我们主要研究该模型中避难所与扩散的作用.首先通过线性化方法和Lypunov方法分别讨论非负常数平衡解的局部和全局渐近稳定性,然后给出交错扩散导致Turing不稳定的一个充分条件,最后,作为一个应用,我们研究一类带HollingⅡ型功能反应项的捕食者-食饵模型.     

一类具有时滞和自食现象的捕食者-食饵征税模型(英文)

研究了一类食饵具有时滞和自食现象的捕食者-食饵征税系统,并在此基础上将税收考虑进去.通过控制税收量来保护资源不被过渡开发,并在适当的假设条件下,讨论了平衡点的存在性.采用RouthHurwitz判别法得到系统正平衡点局部渐近稳定性的条件,以及通过构造Lyapunov函数证明了系统正平衡点是全局渐近稳定的,同时利用Pontrjagin最大值原理给出了最优征税策略,得到了贴现率能够影响捕获种群的利润水平的结论,目的在于既能保护生态系统又能使经济收益达到最大.通过相应的特征方程,分析了时滞对系统的稳定性产生了影响,并得出了当时滞经过τ=τ_O时系统经历Hopf分支的结论.     

脉冲捕获捕食者与食饵具阶段结构的捕食-食饵模型

研究脉冲捕获捕食者与食饵具阶段结构的捕食-食饵模型.利用频闪映射理论,得到食饵灭绝的周期解是全局吸引的;运用时滞脉冲微分方程理论,证明了此系统是持久的.本文的结论为生态保护提供了可靠的策略依据.     

Stochastic analogues of deterministic single-species population models

Although single-species deterministic difference equations have long been used in modeling the dynamics of animal populations, little attention has been paid to how stochasticity should be incorporated into these models. By deriving stochastic analogues to difference equations from first principles, we show that the form of these models depends on whether noise in the population process is demographic or environmental. When noise is demographic, we argue that variance around the expectation is proportional to the expectation. When noise is environmental the variance depends in a non-trivial way on how variation enters into model parameters, but we argue that if the environment affects the population multiplicatively then variance is proportional to the square of the expectation. We compare various stochastic analogues of the Ricker map model by fitting them, using maximum likelihood estimation, to data generated from an individual-based model and the weevil data of Utida. Our demographic models are significantly better than our environmental models at fitting noise generated by population processes where noise is mainly demographic. However, the traditionally chosen stochastic analogues to deterministic models--additive normally distributed noise and multiplicative lognormally distributed noise--generally fit all data sets well. Thus, the form of the variance does play a role in the fitting of models to ecological time series, but may not be important in practice as first supposed.     

Approximate reduction of linear population models governed by stochastic differential equations: application to multiregional models

In this work we develop approximate aggregation techniques in the context of slow-fast linear population models governed by stochastic differential equations and apply the results to the treatment of populations with spatial heterogeneity. Approximate aggregation techniques allow one to transform a complex system involving many coupled variables and in which there are processes with different time scales, by a simpler reduced model with a fewer number of ‘global’ variables, in such a way that the dynamics of the former can be approximated by that of the latter. In our model we contemplate a linear fast deterministic process together with a linear slow process in which the parameters are affected by additive noise, and give conditions for the solutions corresponding to positive initial conditions to remain positive for all times. By letting the fast process reach equilibrium we build a reduced system with a lesser number of variables, and provide results relating the asymptotic behaviour of the first- and second-order moments of the population vector for the original and the reduced system. The general technique is illustrated by analysing a multiregional stochastic system in which dispersal is deterministic and the rate growth of the populations in each patch is affected by additive noise.     

Delay Hill dynamics in regulatory biological systems

We explore one of the best-studied protein circuits in human cells, the negative feedback loop between the tumor suppressor p53 and the oncogene Mdm2 following nuclear irradiation. Using stochastic delay differential equations and the Gillespie algorithm, we illustrate the distinct oscillatory dynamics at the single-cell and population-cell levels which were found in the recent experiments. The oscillatory dynamics of p53-Mdm2 interaction appears as coherent resonance with delay and noise in individual cells. Dephasing mechanisms provide the origin of damped oscillation at the population level out of the sustained one at the single-cell level. The non-Gaussian nature of distributions of protein populations results from the interplay between time delay and nonlinearity of reaction processes. Our findings may lead to new insights related to the effects of noise and cancer therapy.     

Quantifying Stochastic Noise in Cultured Circadian Reporter Cells

Stochastic noise at the cellular level has been shown to play a fundamental role in circadian oscillations, influencing how groups of cells entrain to external cues and likely serving as the mechanism by which cell-autonomous rhythms are generated. Despite this importance, few studies have investigated how clock perturbations affect stochastic noise—even as increasing numbers of high-throughput screens categorize how gene knockdowns or small molecules can change clock period and amplitude. This absence is likely due to the difficulty associated with measuring cell-autonomous stochastic noise directly, which currently requires the careful collection and processing of single-cell data. In this study, we show that the damping rate of population-level bioluminescence recordings can serve as an accurate measure of overall stochastic noise, and one that can be applied to future and existing high-throughput circadian screens. Using cell-autonomous fibroblast data, we first show directly that higher noise at the single-cell results in faster damping at the population level. Next, we show that the damping rate of cultured cells can be changed in a dose-dependent fashion by small molecule modulators, and confirm that such a change can be explained by single-cell noise using a mathematical model. We further demonstrate the insights that can be gained by applying our method to a genome-wide siRNA screen, revealing that stochastic noise is altered independently from period, amplitude, and phase. Finally, we hypothesize that the unperturbed clock is highly optimized for robust rhythms, as very few gene perturbations are capable of simultaneously increasing amplitude and lowering stochastic noise. Ultimately, this study demonstrates the importance of considering the effect of circadian perturbations on stochastic noise, particularly with regard to the development of small-molecule circadian therapeutics.     

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.     

Stochastic growth and extinction in a spatial geometric Brownian population model with migration and correlated noise

A continuous spatial model for populations that are not density-regulated is analyzed. The model is a generalization of the geometric Brownian motion often used to describe populations at a single location. The locations are linked by migration and spatial correlation in the noise. At any point of time, the population size at a given location is log normally distributed so the log population size constitutes a Gaussian field. The model is homogeneous in space but not in time. In particular, we analyze the case when the stochastic growth rate is negative and the total population approaches extinction. The properties of the extinction process is studied by considering local quasi-extinctions. A major conclusion is that migration tends to increase the time to extinction provided that there is no cost of migration. However, as the area occupied by the species starts to decrease, the decrease is faster for populations with larger migration.     

Timing and dynamics of single cell gene expression in the arabinose utilization system

The arabinose utilization system of Escherichia coli displays a stochastic all-or-nothing response at intermediate levels of arabinose, where the population divides into a fraction catabolizing the sugar at a high rate (on-state) and a fraction not utilizing arabinose (off-state). Here we study this decision process in individual cells, focusing on the dynamics of the transition from the off- to the on-state. Using quantitative time-lapse microscopy, we determine the time delay between inducer addition and fluorescence onset of a GFP reporter. Through independent characterization of the GFP maturation process, we can separate the lag time caused by the reporter from the intrinsic activation time of the arabinose system. The resulting distribution of intrinsic time delays scales inversely with the external arabinose concentration, and is compatible with a simple stochastic model for arabinose uptake. Our findings support the idea that the heterogeneous timing of gene induction is causally related to a broad distribution of uptake proteins at the time of sugar addition.     

种群统计随机性和环境随机性对种群绝灭的影响

影响种群绝灭的随机干扰可分为种群统计随机性、环境随机性和随机灾害三大类。在相对稳定的环境条件下和相对较短的时间内,以前两类随机干扰对种群绝灭的影响为生态学家关注的焦点。但是,由于自然种群动态及其影响因子的复杂特征,进一步深入研究随机干扰对种群绝灭的作用在理论上和实践上都必须发展新的技术手段。本文回顾了种群统计随机性与环境随机性的概念起源与发展,系统阐述了其分析方法。归纳了两类随机性在种群绝灭研究中的应用范围、作用方式和特点的异同和区别方法。各类随机作用与种群动态之间关系的理论研究与对种群绝灭机理的实践研究紧密相关。根据理论模型模拟和自然种群实际分析两方面的研究现状,作者提出了进一步深入研究随机作用与种群非线性动态方法的策略。指出了随机干扰影响种群绝灭过程的研究的方向：更多的研究将从单纯的定性分析随机干扰对种群动力学简单性质的作用,转向结合特定的种群非线性动态特征和各类随机力作用特点具体分析绝灭极端动态的成因,以期做出精确的预测。