一类时滞四种群捕食被捕食系统的全局稳定性

对四种群的捕食-被捕食模型,利用解的存在性定理、正性定理、上下解方法和相应的单调迭代序列,研究了一类具有时滞的非线性反应扩散系统的牛曼初边值问题,得到了解的存在性和平衡态方程正解的全局渐近稳定性的充分条件.这个结果隐含着捕食-被捕食系统的共存是持久的,平凡解和所有半平凡解是不稳定的.     

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.     

Multiphase topology optimization with a single variable using the phase-field design method

In this study, a multimaterial topology optimization method using a single variable is proposed by combining the solid isotropic material with penalization method and the reaction-diffusion equation. Unlike ordinary multimaterial optimization, which requires several variables depending on the number of material types, this method intends to represent various materials as one variable. The proposed method combines two special functions in the sensitivity analysis of the objective function to converge the design variable into prespecified density values defined for each of the multimaterials. The composition constraint based on a normal distribution function is also introduced to estimate the distribution of each target density value in a single variable. It enables density exchange between multiple materials by increasing or decreasing the amount of a specific material. The proposed method is applied to structural and electromagnetic problems to verify its effectiveness, and its usefulness is also confirmed from the viewpoint of cost and computation time.     

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。     

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.     

随机时滞反应扩散神经网络的指数稳定性

本文是讨论了一类随机变时滞反应扩散Hopfield神经网络的矩指数稳定性。利用平均Lya- punov泛函方法,随机偏微分方程的Ito公式和时滞微分不等式技巧,证明了随机变时滞反应扩散Hopfield神经网络的平衡解的矩指数稳定性,给出了这类随机变时滞神经网络平衡解矩指数稳定性的实用代数判据,得到了一些新结果。最后,给出了主要定理的一个应用实例。     

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。     

反应扩散方程的奇异摄动问题的最小二乘的有限元方法

For a kind of the singularly perturbed reaction-diffusion problem, the standard energy norm is too weak to measure adequately the errors of solutions computed by finite element methods. The multiplier of this problem gives an unbalanced norm whose different components have different orders of convergence. In the paper, we introduce a new stronger norm, construct the least-squares finite element method (LSFEM) in this new norm and develop a robust and stable numerical approach for more general singularly perturbed reaction-diffusion problems in 1D spaces. At last, numerical examples are presented to illustrate the proposed method and theoretical results.     

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.