具有毒素影响的二维Kolmogorov模型的持续生存和绝灭

研究了具有毒素影响的二维Kolmogorov模型,给出了该系统持续生存与绝灭的充分条件.     

随机时滞Lotka-Volterra模型数值解的收敛性

通常情况下,随机时滞Lotka-Volterra模型没有解析解,因而数值逼近方法是研究其性质的有效工具.本文根据Euler数值方法,利用鞅不等式和Ito公式讨论了一类随机时滞Lotka-Volterra模型数值解的收敛性,给出了数值解收敛于解析解的条件.最后通过数值算例对数值计算方法进行了验证.     

一类具有时滞的传染病模型的稳定性分析

研究了一类具有时滞的传染病生物模型．首先研究了该模型的线性稳定性,并给出了一列Hopf分支值,然后利用中心流形定理和正规型方法,给出了确定分支周期解的分支方向与稳定性的计算公式．     

Stochastic Sensitivity Analysis and Kernel Inference via Distributional Data

Cellular processes are noisy due to the stochastic nature of biochemical reactions. As such, it is impossible to predict the exact quantity of a molecule or other attributes at the single-cell level. However, the distribution of a molecule over a population is often deterministic and is governed by the underlying regulatory networks relevant to the cellular functionality of interest. Recent studies have started to exploit this property to infer network states. To facilitate the analysis of distributional data in a general experimental setting, we introduce a computational framework to efficiently characterize the sensitivity of distributional output to changes in external stimuli. Further, we establish a probability-divergence-based kernel regression model to accurately infer signal level based on distribution measurements. Our methodology is applicable to any biological system subject to stochastic dynamics and can be used to elucidate how population-based information processing may contribute to organism-level functionality. It also lays the foundation for engineering synthetic biological systems that exploit population decoding to more robustly perform various biocomputation tasks, such as disease diagnostics and environmental-pollutant sensing.     

Stochastic Sensitivity Analysis and Kernel Inference via Distributional Data

Cellular processes are noisy due to the stochastic nature of biochemical reactions. As such, it is impossible to predict the exact quantity of a molecule or other attributes at the single-cell level. However, the distribution of a molecule over a population is often deterministic and is governed by the underlying regulatory networks relevant to the cellular functionality of interest. Recent studies have started to exploit this property to infer network states. To facilitate the analysis of distributional data in a general experimental setting, we introduce a computational framework to efficiently characterize the sensitivity of distributional output to changes in external stimuli. Further, we establish a probability-divergence-based kernel regression model to accurately infer signal level based on distribution measurements. Our methodology is applicable to any biological system subject to stochastic dynamics and can be used to elucidate how population-based information processing may contribute to organism-level functionality. It also lays the foundation for engineering synthetic biological systems that exploit population decoding to more robustly perform various biocomputation tasks, such as disease diagnostics and environmental-pollutant sensing.     

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．     

在杀虫剂作用下的一类具有Allee效应的天敌-害虫模型

对一类具有Allee效应的天敌-害虫模型作了理论分析,同时对在杀虫剂作用下的此系统又作了理论分析,比较了二者之间的区别,从而从理论上获知利用杀虫剂控制虫害的利弊．     

Genetic Diversity in Introduced Populations with an Allee Effect

A phenomenon that strongly influences the demography of small introduced populations and thereby potentially their genetic diversity is the demographic Allee effect, a reduction in population growth rates at small population sizes. We take a stochastic modeling approach to investigate levels of genetic diversity in populations that successfully overcame either a strong Allee effect, in which populations smaller than a certain critical size are expected to decline, or a weak Allee effect, in which the population growth rate is reduced at small sizes but not negative. Our results indicate that compared to successful populations without an Allee effect, successful populations with a strong Allee effect tend to (1) derive from larger founder population sizes and thus have a higher initial amount of genetic variation, (2) spend fewer generations at small population sizes where genetic drift is particularly strong, and (3) spend more time around the critical population size and thus experience more genetic drift there. In the case of multiple introduction events, there is an additional increase in diversity because Allee-effect populations tend to derive from a larger number of introduction events than other populations. Altogether, a strong Allee effect can either increase or decrease genetic diversity, depending on the average founder population size. By contrast, a weak Allee effect tends to decrease genetic diversity across the entire range of founder population sizes. Finally, we show that it is possible in principle to infer critical population sizes from genetic data, although this would require information from many independently introduced populations.     

Parametric Sensitivity Analysis of Oscillatory Delay Systems with an Application to Gene Regulation

A parametric sensitivity analysis for periodic solutions of delay-differential equations is developed. Because phase shifts cause the sensitivity coefficients of a periodic orbit to diverge, we focus on sensitivities of the extrema, from which amplitude sensitivities are computed, and of the period. Delay-differential equations are often used to model gene expression networks. In these models, the parametric sensitivities of a particular genotype define the local geometry of the evolutionary landscape. Thus, sensitivities can be used to investigate directions of gradual evolutionary change. An oscillatory protein synthesis model whose properties are modulated by RNA interference is used as an example. This model consists of a set of coupled delay-differential equations involving three delays. Sensitivity analyses are carried out at several operating points. Comments on the evolutionary implications of the results are offered.     

Noise-Induced Coherence and Network Oscillations in a Reduced Bursting Model

The dynamics of the Hindmarsh-Rose (HR) model of bursting thalamic neurons is reduced to a system of two linear differential equations that retains the subthreshold resonance properties of the HR model. Introducing a reset mechanism after a threshold crossing, we turn this system into a resonant integrate-and-fire (RIF) model. Using Monte-Carlo simulations and mathematical analysis, we examine the effects of noise and the subthreshold dynamic properties of the RIF model on the occurrence of coherence resonance (CR). Synchronized burst firing occurs in a network of such model neurons with excitatory pulse-coupling. The coherence level of the network oscillations shows a stochastic resonance-like dependence on the noise level. Stochastic analysis of the equations shows that the slow recovery from the spike-induced inhibition is crucial in determining the frequencies of the CR and the subthreshold resonance in the original HR model. In this particular type of CR, the oscillation frequency strongly depends on the intrinsic time scales but changes little with the noise intensity. We give analytical quantities to describe this CR mechanism and illustrate its influence on the emerging network oscillations. We discuss the profound physiological roles this kind of CR may have in information processing in neurons possessing a subthreshold resonant frequency and in generating synchronized network oscillations with a frequency that is determined by intrinsic properties of the neurons. PACS 05.45.-a, 05.40.Ca, 87.18.Sn, 87.19     

The Effect of Time Delay in a Two-Patch Model with Random Dispersal

We consider a two-patch model for a single species with dispersal and time delay. For some explicit range of dispersal rates, we show that there exists a critical value τ _c for the time delay τ such that the unique positive equilibrium of the system is locally asymptotically stable for τ∈[0,τ _c ) and unstable for τ>τ _c .     

Probability of Disease Extinction or Outbreak in a Stochastic Epidemic Model for West Nile Virus Dynamics in Birds

Acta Biotheoretica - Thresholds for disease extinction provide essential information for the prevention and control of diseases. In this paper, a stochastic epidemic model, a continuous-time Markov...     

Contest and Scramble Competition and the Carry-Over Effect in Globodera spp. in Potato-Based Crop Rotations Using an Extended Ricker Model

The Ricker model extended with a linear term was used to model the dynamics of a potato cyst nematode population on different potato cultivars over a wide range of population densities. The model accounts for contest and scramble competition and between-year carryover of unhatched eggs. Contest competition occurs due to the restricted amount of available root sites that are the feeding source of the female nematode. Nematodes not reaching such a feeding site turn into males and do not contribute to a new generation. Scramble competition results in a decrease of the number of eggs per cyst at high densities due to the decrease in the food supply per feeding site. At still higher densities, the size of the root system declines; then dynamics are mostly governed by carryover of cysts between subsequent years. The restricted number of three parameters in the proposed model made it possible to calculate the equilibrium densities and to obtain analytical expressions of the model''s sensitivity to parameter change. The population dynamics model was combined with a yield-loss assessment model and, using empirical Bayesian methods, was fitted to data from a 3-year experiment carried out in the Netherlands. The experiment was set up around the location of a primary infestation of Globodera pallida in reclaimed polder soil. Due to a wide range of population densities at short distances from the center of the infestation, optimal conditions existed for studying population response and damage in different cultivars. By using the empirical Bayesian methods it is possible to estimate all parameters of the dynamic system, in contrast to earlier studies with realistic biological models where convergence of parameter estimation algorithms was a problem. Applying the model to the outcome of the experiment, we calculated the minimum gross margin that a fourth crop needs to reach in order to be taken up in a 3-year rotation with potato. An equation was derived that accounted for both gross margin changes and nematode-related yield loss. The new model with its three parameters has the right level of complexity for the amount and type of collected data. Two other important models from the literature, containing five and 10 parameters respectively, may at this point turn out to be less appropriate. Consequences for research priorities are discussed and prediction schemes are taken in consideration.     

Sudden Shifts in Ecological Systems: Intermittency and Transients in the Coupled Ricker Population Model

Many real ecological systems show sudden changes in behavior, phenomena sometimes categorized as regime shifts in the literature. The relative importance of exogenous versus endogenous forces producing regime shifts is an important question. These forces’ role in generating variability over time in ecological systems has been explored using tools from dynamical systems. We use similar ideas to look at transients in simple ecological models as a way of understanding regime shifts. Based in part on the theory of crises, we carefully analyze a simple two patch spatial model and begin to understand from a mathematical point of view what produces transient behavior in ecological systems. In particular, since the tools are essentially qualitative, we are able to suggest that transient behavior should be ubiquitous in systems with overcompensatory local dynamics, and thus should be typical of many ecological systems. This work has been supported by NSF Grant EF-0434266.     

Allee Effect and Control of Lake System Invasion

We consider the model of invasion prevention in a system of lakes that are connected via traffic of recreational boats. It is shown that in presence of an Allee effect, the general optimal control problem can be reduced to a significantly simpler stationary optimization problem of optimal invasion stopping. We consider possible values of model parameters for zebra mussels. The general N-lake control problem has to be solved numerically, and we show a number of typical features of solutions: distribution of control efforts in space and optimal stopping configurations related with the clusters in lake connection structure.     

The Allee Effect in Population Dynamics with a Seasonal Reproduction Pattern

The local consequences of the Allee effect in isolated populations of animal species with a seasonal reproduction pattern that nonmonotonically depends on population density are studied based on a discrete analog of the Bazykin–Ludwig model. Along with the critical population size (below which the population degenerates because of the Allee effect), the limiting population size is discovered: the population with a higher density degenerates because of overpopulation. The effect of the initial population size on possible scenarios of its development is studied in detail. It is shown that an “intermediate” population size that provides the maximum population density is unachievable in some cases.     

一类带有隔离项和分布时滞的SIQS模型的稳定性分析

研究了一类带有隔离项和分布时滞的SIQS模型,利用局部线性化方法并构造了适当的Liapunov函数,获得了该系统平衡点的稳定性结论.