Existence and linear stability of planar waves in the Oregonator model

In this paper,various waves in the Oregonator model are investigated in detail.The existence of planar waves(in particular,spiral waves)is rigorously proven and their linear stability is analysed.In addition,some non-planar waves in the model are also presented.     

噪声诱导的连贯切换

以著名的基因开关系统为例, 数值地调查了噪声对其双稳性的影响. 发现基因调控过程中的合成率或降解率的涨落所导致的噪声以及环境涨落引起的噪声均能够诱导连贯切换, 而且发现存在一个最合适的噪声强度, 它不仅能实现这种切换, 而且能使弱信号被最优地扩大. 此外,还发现由Poisson τ-跳跃算法所引入的内部噪声不能够诱导上述切换.     

Modeling of intercellular synchronization in the Drosophila circadian clock

In circadian rhythm generation,intercellular signaling factors are shown to play a crucial role in both sustaining intrinsic cellular rhythmicity and acquiring collective behaviours across a population of circadian neurons.However,the physical mechanism behind their role remains to be fully understood.In this paper,we propose an indirectly coupled multicellular model for the synchronization of Drosophila circadian oscillators combining both intracellular and intercellular dynamics.By simulating different experimental conditions,we find that such an indirect coupling way can synchronize both heterogeneous self-sustained circadian neurons and heterogeneous mutational damped circadian neurons.Moreover,they can also be entrained to ambient light-dark(LD) cycles depending on intercellular signaling.     

EXPLICIT REPRESENTATION OF PLANAR WAVE SPEED AND DISPERSIVE RELATION IN GENERAL EXCITABLE MEDIA

We transform the problem of seeking the planar wave speed in general excitable media into a cubically algbraic equation, thus we can find the explicit representation of the planar wave speed (in one-dimensional case, the traveling wave speed) and dispersive relation. Especially for a few typical excitable media, we give the formula for calculating the corresponding wave speed.     

KINETICS OF THE WAVETRAIN IN THE TWO-VARIABLE OREGONATOR MODEL

In this paper we first discuss the asymptotic behaviours of solitary impulses in reaction-diffusion equations of Oregonator under the equal, single and double diffusion conditions, respectively. Then we obtain the asymptotic equations of motion of wavetrains for this model by a superposition of solitary impulses, and finally we analyse the stability of wavetrains.     

对称耦合振子中同相解的稳定性

本文研究了一类耦合系统中同相解的稳定性,并给出了耦合Oregon振子中同相解 稳定性的充分条件.     

激励介质中波的运动方程

本文从数学方面,建立了一种运动坐标系,运用摄动方法,得到了二维,三维激励介质中波的运动方程,它为研究激励介质中各种波形解奠定了基础,也给进一步进行理论分析带来了方便。     

耦合俄勒冈振子的正定态,特征值及相内解

本文同了耦合俄勒冈振子下列研究结果：（１）均匀正定态的存在唯一性；（２）耦合振子与单个振子特征值之间的关系；（３）相内解的存在性。