Parameter estimation for a morphochemical reaction-diffusion model of electrochemical pattern formation

The process of electrodeposition can be described in terms of a reaction-diffusion partial differential equation (PDE) system that models the dynamics of the morphology profile and the chemical composition. Here we fit such a model to the different patterns present in a range of electrodeposited and electrochemically modified alloys using PDE constrained optimization. Experiments with simulated data show how the parameter space of the model can be divided into zones corresponding to the different physical patterns by examining the structure of an appropriate cost function. We then use real data to demonstrate how numerical optimization of the cost function can allow the model to fit the rich variety of patterns arising in experiments. The computational technique developed provides a potential tool for tuning experimental parameters to produce desired patterns.     

一类具有时滞的食饵-捕食者模型的时空斑图

研究了一类具有时滞和反应扩散的食饵-捕食者模型的动力学行为.通过数学分析,发现了两种不同类型的不稳定性,并且详细给出了图灵不稳定的条件.在由反应扩散引起的不稳定的条件下,通过一系列的数值模拟,得到了参数空间中丰富的图灵结构,分别有点状斑图、条状斑图以及点状和条状共存的斑图结构.在由时滞引起的不稳定的条件下,通过数值模拟,得到了"黑眼斑图".这些结果表明,受时滞和扩散影响的模型具有丰富的动力学,揭示了该模型在实际生活中是非常有用的.     

具反应扩散混合时滞Cohen-Grossberg神经网络的指数耗散性

利用扩散算子特性、M-矩阵性质和不等式分析技巧,在不要求神经网络激励函数的有界性、单调性、可微性以及平均时滞有界性的弱保守条件下,研究了一类具有反应扩散混合时滞的非自治Cohen-Grossberg神经网络的实不变集、全局指数稳定性和指数耗散性,并给出了相关的充分性条件.文中所使用的方法摒弃了常规构造适当的Lyapunov泛函的方法,克服了Lyapunov泛函难构造的困难,且得到的结果扩展和改进了其他文献结果.最后给出了一个数值例子来说明所得结果的有效性.     

Mean square exponential stability of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays

In this paper, we establish a method to study the mean square exponential stability of the zero solution of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays. By using the properties of M-cone and inequality technique, we obtain some sufficient conditions ensuring mean square exponential stability of the zero solution of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays. The sufficient conditions are easily checked in practice by simple algebra methods and have a wider adaptive range. Two examples are also discussed to illustrate the efficiency of the obtained results.     

一类基于反应扩散方程的连续源水污染模型

考虑具有初边值条件情况的水污染连续源模型,以反应扩散方程的形式建立模型进行模拟,并根据偏微分方程的常用解法求出解析解.     

具有放牧率的两种群竞争扩散模型的概周期解及其稳定性

本文对具有放牧率的两种竞争扩散模型的概周期解进行了讨论，采用比较原理，Ｓｃｈａｕｄｅｒ不动点定理及Ｌｙａｐｕｎｏｖ函数方法，得到了空间齐次概周期解的存在性和稳定性的一些简捷的充分条件。     

一类多维反应扩散方程组初边值问题整体强解的存在唯一性

研究从生物物理学中提出的一类反应扩散方程组的初边值问题,通过对非线性项作出增长性、有界性和连续性的假设,利用近似解的积分估计和Galerkin方法证明了整体强解的存在性,并证明了解的唯一性.其结果说明了解的存在时间为0～∞,并为数值求解提供了可能性和理论基础.     

多时滞反应扩散Cohen-Grossberg神经网络的稳定性

研究了一类具有反应扩散项的时滞Cohen—Grossberg神经网络模型利用拓扑度理论和Lyapunov函数方法，研究了此类系统平衡点的存在性及全局指数稳定性，给出了判定定理．     

The evolution of travelling waves from chemical-clock reactions

A clock-reaction is a chemical reaction which gives rise to an initial induction period before a significant change in concentration of one of the chemical species occurs. In this paper the development of travelling waves from a particular class of inhibited autocatalytic clock-reactions is analysed. The numerical solutions show that, after the induction period, a propagating reaction-diffusion front is initiated. This front is seen to accelerate initially and then to become a constant-speed travelling wave. An asymptotic analysis of the large-time travelling-wave behaviour is given and from this it is possible to fix a minimum wave speed. The asymptotic predictions of the wave speed are found to agree well with those of the numerical solution.     

受平衡约束的平行反应体系的催化剂粒内反应-扩散过程模拟

以甲烷化体系为例，研究了受平衡约束的平行反应的催化剂粒内状态。采用正交配置法求解催化剂的一维、二维反应－扩散非等温模型。模拟结果表明，由于甲烷化反应与变换反应交互作用，导致变换反应在催化剂粒内正、逆反应均存在。内扩散效率因子不能准确描述催化剂内表面利用率，应考虑粒内参数分布。