Nonlinear time series analysis of jerk congenital nystagmus

Nonlinear dynamics provides a complementary framework to control theory for the quantitative analysis of the oculomotor control system. This paper presents a number of findings relating to the aetiology and mechanics of the pathological ocular oscillation jerk congenital nystagmus (jerk CN). A range of time series analysis techniques were applied to recorded jerk CN waveforms, and also to simulated jerk waveforms produced by an established model in which the oscillations are a consequence of an unstable neural integrator. The results of the analysis were then interpreted within the framework of a generalised model of the unforced oculomotor system. This work suggests that for jerk oscillations, the origin of the instability lies in one of the five oculomotor subsystems, rather than in the final common pathway (the neural integrator and muscle plant). Additionally, experimental estimates of the linearised foveation dynamics imply that a refixating fast phase induced by a near-homoclinic trajectory will result in periodic oscillations. Local dimension calculations show that the dimension of the experimental jerk CN data increases during the fast phase, indicating that the oscillations are not periodic, and hence that the refixation mechanism is of greater complexity than a homoclinic reinjection. The dimension increase is hypothesised to result either from a signal-dependent noise process in the saccadic system, or the activation of additional oculomotor components at the beginning of the fast phase. The modification of a recent saccadic system model to incorporate biologically realistic signal-dependent noise is suggested, in order to test the first of these hypotheses. Action Editor: Peter Latham     

Statistical techniques for detection of major genes in animal breeding data

Summary Statistical techniques for detection of major loci and for making inferences about major locus parameters such as genotypic frequencies, effects and gene action from field-collected data are presented. In field data, major genotypic effects are likely to be masked by a large number of environmental differences in addition to additive and nonadditive polygenic effects. A graphical technique and a procedure for discriminating among genetic hypotheses based on a mixed model accounting for all these factors are proposed. The methods are illustrated by using simulated data.Journal Paper No. J-12733 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 1901     

Global stability of stationary solutions to a nonlinear diffusion equation in phytoplankton dynamics

We consider a nonlinear diffusion equation proposed by Shigesada and Okubo which describes phytoplankton growth dynamics with a selfs-hading effect.We show that the following alternative holds: Either (i) the trivial stationary solution which vanishes everywhere is a unique stationary solution and is globally stable, or (ii) the trivial solution is unstable and there exists a unique positive stationary solution which is globally stable. A criterion for the existence of positive stationary solutions is stated in terms of three parameters included in the equation.     

The stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays and reaction–diffusion terms

The global asymptotic stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays and reaction–diffusion terms is investigated. Under some suitable assumptions and using Lyapunov–Krasovskii functional method, we apply the linear matrix inequality technique to propose some new sufficient conditions for the global asymptotic stability of the addressed model in the stochastic sense. The mixed time delays comprise both the time-varying and continuously distributed delays. The effectiveness of the theoretical result is illustrated by a numerical example.     

陆地表层系统动力学机制研究Ⅰ．──陆地表层系统和动力学方程

对陆地表层动力学的研究对象、研究内容及其基本理论方法作了阐述,以多学科综合的观点定义了陆地表层系统,包括时空尺度范围的约定、状态变量的选择、物质循环以及外界因子等的讨论;依据物质和能量守恒原理建立了陆地表层系统的非线性控制方程组,表述了各圈层之间物质循环和能量循环过程、反馈关系及其动力学联系;讨论了控制方程组的整体运作功能以及人类活动对陆地表层系统的影响．     

A deterministic analysis of self-incompatibility alleles

A number of plant species have a self-incompatibility locus that prevents self-fertilization. We 'analyse a deterministic model with an arbitrary number of alleles. We prove that the only polymorphic equilibrium is the one for which all (heterozygous) genotypes are equally frequent, and we prove that all (initially) polymorphic populations converge to this equilibrium.     

Comparison of life history traits between invasive and native populations of purple loosestrife (Lythrum salicaria) using nonlinear mixed effects model

We compared growth patterns of invasive and native populations of purple loosestrife (Lythrum salicaria) while varying water and nutrient levels. We examined three life-history traits (height, number of branches, and the size of largest leaf) during the growth period adopting a nonlinear mixed effects model. Invasive populations were found to be slower in shoot elongation but grew to be taller than native populations. Invasive populations produced more branches than natives only in the high water, high nutrient treatment. Invasive populations had a similar increase in the size of the largest leaf compared to natives, but ultimately produced a greater size of largest leaf than natives. Invasive populations were found to display a greater vegetative expansion, but this was not strongly affected by our treatments.     

具有阶段结构和非线性接触率的SI传染病模型的渐近性态

研究了一类具有阶段结构和非线性接触率的传染病模型的渐近性态,得到了传染病最终消除和成为地方病的阀值．