Stochastic resonance in circadian rhythms

The effect of fluctuations in the two-variable discrete delay model proposed earlier by us [1] for the circadian rhythm of the fungal species Neurospora Crassa is studied. We have investigated the effect of parametric and additive noise in two different regimes namely, steady-state and Period-1 regimes. It is found that under the influence of noise coherent oscillations are generated in the steady-state. Oscillations are preserved and robust to a wide range of noise intensity in the Period-1 regime. The oscillations in both these regimes are always found to be close to the circadian period (21.5 h). Coherence resonance is observed when parametric or velocity additive noise is added near the Hopf bifurcation. Finally, the implications of fluctuations in circadian rhythms are discussed. This article is dedicated to Professor Karl Jug on the occassion of his sixtyfifth birthday.     

Coexistence and stability of predator-prey model with Beddington-DeAngelis functional response and stage structure

We present a predator-prey model of Beddington-DeAngelis type functional response with stage structure on prey. The constant time delay is the time taken from birth to maturity about the prey. By the uniform persistence theories and monotone dynamic theories, sharp threshold conditions which are both necessary and sufficient for the permanence and extinction of the model as well as the sufficient conditions for the global stability of the coexistence equilibria are obtained. Biologically, it is proved that the variation of prey stage structure can affect the permanence of the system and drive the predator into extinction by changing the prey carrying capacity: Our results suggest that the predator coexists with prey permanently if and only if predator's recruitment rate at the peak of prey abundance is larger than its death rate; and that the predator goes extinct if and only if predator's possible highest recruitment rate is less than or equal to its death rate; furthermore, our results also show that a sufficiently large mutual interference by predators can stabilize the system.     

ENERGY ESTIMATES FOR DELAY DIFFUSION-REACTION EQUATIONS

In this paper we consider nonlinear delay diffusion-reaction equations with initial and Dirichlet boundary conditions. The behaviour and the stability of the solution of such initial boundary value problems （IBVPs） are studied using the energy method. Simple numerical methods are considered for the computation of numerical approximations to the solution of the nonlinear IBVPs. Using the discrete energy method we study the stability and convergence of the numerical approximations. Numerical experiments are carried out to illustrate our theoretical results.     

一类n阶非线性时滞微分方程周期解的存在性

通过应用拓扑度的方法, 获得了一类n阶非线性时滞微分方程2π周期解存在性的若干结论.     

Periodic Duffing delay equations with state dependent impulses

Conditions are obtained for the Duffing equation with delay and state dependent impulses to admit a periodic solution.     

GOLDEN AGES OR MAGIC MOMENTS?

ABSTRACT. The paper is an attempt to refute Quinn's ‘the Golden Age of fisheries population models has ended “hypothesis. The approach is to show it is possible to provide simple matrix based theory for use with delay difference equations applied to products of the 0th to 4th powers of length and numbers at length (Alias” proto‐moments“). It compares these to models just based upon numbers and biomass. It also shows examples (of comparatively little moment) indicating how using multiple proto‐moments could improve the ability of delay difference equations to handle the size dependent processes of maturity, selection, natural mortality rates and predation rates and thus improving the biological reality of these models.     

Permanence for non-autonomous food chain systems with delay

In this paper we first establish a new general criterion for the permanence of Kolmogorov-type systems of nonautonomous functional differential equations. Then, as applications of this criterion we study the permanence of a class of n-species general nonautonomous food chain systems with delay and new sufficient condition are established.     

高阶非线性时滞差分方程解的渐近性

研究如下的具强迫项的高阶非线性时滞差分方程△^my(n) u(n)l↑∑i=1 gi(y(n-τ))=v(n)其中，m≥1，u,v：N→R，gi：R→R且τ∈{0，1，2，3，…)，i=1，2，…，l，得到了使该方程的解具有某种渐近性态的充分条件。     

激光触发SF6-N2混合气体开关的数值模拟

 在气体放电物理的基础上，对SF₆和N₂采用双光子电离模型，对碳氢化合物的光电离采用3能级模型，并考虑了混合气体的热电离和激光对气体的欧姆加热作用，建立了激光触发SF₆-N₂混合气体开关的数值模型，模拟了激光触发SF6-N2混合气体多级间隙开关实验。激光触发延迟时间的计算值与实验结果符合较好。理论计算表明：激光触发SF₆-N₂混合气体间隙开关的延迟时间随SF₆含量的增加呈上升趋势，而随激光脉冲能量、充气压力等的上升呈下降趋势。     

Pseudospectra and stability radii for analytic matrix functions with application to time-delay systems

Definitions for pseudospectra and stability radii of an analytic matrix function are given, where the structure of the function is exploited. Various perturbation measures are considered and computationally tractable formulae are derived. The results are applied to a class of retarded delay differential equations. Special properties of the pseudospectra of such equations are determined and illustrated.