具有放牧率的某些概周期生态模型

文［１］研究了具有放牧率的周期生态模型的周期解的存在性、唯一性与稳定性等问题．本文考虑更加广泛的生态模型,即具有放牧率的概周期生态系统的概周期解的存在性、稳定性,通过利用指数型二分性和不动点方法,得到一些新结果．     

Neural fields with fast learning dynamic kernel

We introduce a modified-firing-rate model based on Hebbian-type changing synaptic connections. The existence and stability of solutions such as rest state, bumps, and traveling waves are shown for this type of model. Three types of kernels, namely exponential, Mexican hat, and periodic synaptic connections, are considered. In the former two cases, the existence of a rest state solution is proved and the conditions for their stability are found. Bump solutions are shown for two kinds of synaptic kernels, and their stability is investigated by constructing a corresponding Evans function that holds for a specific range of values of the kernel coefficient strength (KCS). Applying a similar method, we consider exponential synaptic connections, where traveling wave solutions are shown to exist. Simulation and numerical analysis are presented for all these cases to illustrate the resulting solutions and their stability.     

Analysis of a time-delayed mathematical model for tumour growth with an almost periodic supply of external nutrients

In this paper, the existence, uniqueness and exponential stability of almost periodic solutions for a mathematical model of tumour growth are studied. The establishment of the model is based on the reaction–diffusion dynamics and mass conservation law and is considered with a delay in the cell proliferation process. Using a fixed-point theorem in cones, the existence and uniqueness of almost periodic solutions for different parameter values of the model is proved. Moreover, by the Gronwall inequality, sufficient conditions are established for the exponential stability of the unique almost periodic solution. Results are illustrated by computer simulations.     

具常数时滞细胞神经网络概周期解

利用矩阵不等式的分析技巧和Banach空间中不动点定理,得到了具常数时滞细胞神经网络概周期解的存在性、唯一性和全局指数稳定性,推广和改进了已有文献的结论。     

变时滞SIS流行病模型的稳定性分析

研究了一类时滞SIS流行病模型,分析了该模型无病平衡点和地方平衡点的存在性,得到了无病平衡点全局指数渐近稳定和地方病平衡点局部指数渐近稳定的充分条件,同时给出了地方病平衡点吸引区域的估计。     

Unconditional global exponential stability in Lagrange sense of genetic regulatory networks with SUM regulatory logic

In this paper, the global exponential stability in Lagrange sense for genetic regulatory networks (GRNs) with SUM regulatory logic is firstly studied. By constructing appropriate Lyapunov-like functions, several criteria are presented for the boundedness, ultimate boundedness and global exponential attractivity of GRNs. It can be obtained that GRNs with SUM regulatory logic are unconditionally globally exponentially stable in Lagrange sense. These results can be applied to analyze monostable as well as multistable networks. Furthermore, to analyze the stability for GRNs more comprehensively, the existence of equilibrium point of GRNs is proved, and some sufficient conditions of the global exponential stability in Lyapunov sense for GRNs are derived. Finally two numerical examples are given to illustrate the application of the obtained results.     

On the existence of stable pairing distributions

We formulate and analyze pair-formation models for multiple groups with general pairing rates and arbitrary mixing probabilities. Under the assumption of constant recruitment rates and equal average duration of all types of partnerships, we have shown that the dynamics are relatively simple because of the monotonicity properties of the dynamical system associated with the pairing/mixing of heterogeneous populations of male and female individuals. In fact, we have shown that the corresponding asymptotic stable paired distribution is given precisely by the asymptotic values of the matrices that prescribe the mixing/contact structure. In other words, if the sizes of the mixing subpopulations of males and females are asymptotically constant and if the average durations of partnerships are about the same regardless of type, then the matrices that describe the mixing between subpopulations also characterize the distribution of paired types. Alternatively, if the distribution of the average duration of relationships between individuals has a large variance then it may be impossible to detect any relationship between the mixing/contact structure and the observed distribution of paired types. The study of models with constant per-capita recruitment rates give rise to homogeneous systems of degree one. The analysis of the dynamics of pairs for models with exponentially growing populations of singles is complicated. So far, we are only able to classify the stability of all non-strictly positive boundary exponential solutions. From our incomplete analysis, it is not possible to detect necessary and sufficient conditions for the existence and stability of strictly interior exponential solutions. We cannot rule out the possibility of oscillations. The mathematical problems associated with the stability of exponential solutions of dynamical systems of degree one are of relevance in demography, epidemiology, and population dynamics.On leave from University of Alabama in Huntsville     

Global asymptotic behaviour of positive solutions to a non-autonomous Nicholson's blowflies model with delays

This paper addresses the global existence and global asymptotic behaviour of positive solutions to a non-autonomous Nicholson's blowflies model with delays. By using a novel approach, sufficient conditions are derived for the existence and global exponential convergence of positive solutions of the model without any restriction on uniform positiveness of the per capita dead rate. Numerical examples are provided to illustrate the effectiveness of the obtained results.     

一类复杂生态系统的周期解及其稳定性

本文研究了一类复杂生态系统,得到了保证其存在唯一周期解及渐近稳定的充分条件。     

多比例时滞细胞神经网络的指数周期性与稳定性

研究了一类具多比例时滞细胞神经网络的全局指数周期性与稳定性.通过变换y(t)=x(e~t)将具多比例时滞的细胞神经网络变换成具常时滞变系数的细胞神经网络,利用一些分析技巧与构造合适的Lyapunov泛函,得到系统的周期解存在唯一且全局指数周期的时滞依赖的充分条件,判断方法简单易验证.并给出了两个例子及其数值仿真结果以支持所得结论.     

具有时滞的细胞神经网络模型的全局指数稳定性

利用拓扑度理论、推广的Halanaly矩阵时滞微分不等式、Lyapunov原理以及Dini导数,研究了具有时滞的细胞神经网络模型的全局指数稳定性．去掉了有关文献中要求输出函数fj在实数集R上有界、可微的条件,给出了更弱的判定平衡点的存在唯一性以及全局指数稳定性的判据,推广和改进了前人的相关结论,最后的数值例子说明本文结果不仅保守性小,而且计算简单．     

New criteria of almost periodic solution for bam neural networks with delays and impulsive effects

This paper presents some sufficient conditions for the existence and global exponential stability of the almost periodic solution for impulsive bi-directional associative memory neural networks with time-varying delays by using Lyapunov functional and Gronwall-Bellmans inequality technique. Comparing with known literatures, the results of this paper are new and they complement previously known results.     

一类具年龄结构和接种的非终生免疫型传染病模型

研究一类具年龄结构和接种的非终生免疫SIRS传染病模型平衡解的稳定性.首先利用特征线法讨论了模型平衡解的存在性,然后利用比较定理和逐次迭代法得到无病平衡解与地方病平衡解全局稳定性的充分条件.     

On the Role of Schistosome Mating Structure in the Maintenance of Drug-resistant Strains

The effects of drug treatment of human hosts on a population of schistosome parasites depends on a variety of factors. Previous models have shown that multiple strains of drug-resistant parasites are likely to be favored as the treatment rate increases. However, such models have neglected to account for the complex nature of schistosome mating biology. To more accurately account for the biology of these parasites, a simple mating structure is included in a multi-strain schistosome model, with parasites under the influence of drug treatment of their human hosts. Parasites are assumed to pay a cost for drug resistance in terms of reduced reproduction and transmission. The dynamics of the parasite population are described by a system of homogeneous differential equations, and the existence and stability of the exponential solutions for this system are used to infer the impact of drug treatment on the maintenance of schistosome genetic diversity.     

On the role of schistosome mating structure in the maintenance of drug resistant strains

The effects of drug treatment of human hosts upon a population of schistosome parasites depend upon a variety of factors. Previous models have shown that multiple strains of drug-resistant parasites are likely to be favored as the treatment rate increases. However, such models have neglected to account for the complex nature of schistosome mating biology. To more accurately account for the biology of these parasites, a simple mating structure is included in a multi-strain schistosome model, with parasites under the influence of drug treatment of their human hosts. Parasites are assumed to pay a cost for drug resistance in terms of reduced reproduction and transmission. The dynamics of the parasite population are described by a system of homogeneous differential equations, and the existence and stability of the exponential solutions for this system are used to infer the impact of drug treatment on the maintenance of schistosome genetic diversity.     

A delayed neural network method for solving convex optimization problems

In this paper, the delayed projection neural network for a class of solving convex programming problem is proposed. The existence of solution and global exponential stability of the proposed network are proved, which can guarantee to converge at an exact optimal solution of the convex programming problems. Several examples are given to show the effectiveness of the proposed network.     

Existence and stability of travelling wave solutions of a nonlinear integral operator

In this paper, we establish the existence and stability property of travelling wave solutions of a nonlinear integral operator in the inferior case.     

一类具变时滞的模糊BAM神经网络的平衡点的指数稳定性(英文)

研究一类具变时滞的模糊BAM神经网络.利用拓扑度论和微分不等式,获得了该类网络平衡点的存在性、唯一性和全局指数稳定性的充分条件.一个例子用来解释本文获得的结果.     

Predator-prey systems with a perturbed periodic carrying capacity

In this paper we perturb the constant carrying capacity of a predatorprey model. Non-critical cases and critical cases are investigated for existence and stability of periodic solutions.     

Existence and global exponential stability of periodic solution of a class of impulsive networks with infinite delays

Sufficient conditions are obtained for the existence and global exponential stability of a unique periodic solution of a class of impulsive tow-neuron networks with variable and unbounded delays. The approaches are based on Mawhin's continuation theorem of coincidence degree theory and Lyapunov functions.