平面自治系统的规范型与闭轨族周期的临界点

本文通过平面复自治系统的规范型研究实系统具有可线性化的中心和鞍点的条件,定义了k-阶广义细中心及其判定量,给出了计算判定量的递推公式,并对三次系统,讨论了周期的临界点分枝问题.     

Stability of a class of neural network models with delay

ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙ,ｔｈｅｏｒｅｔｉｃａｌａｎｄａｐｌｉｅｄｓｔｕｄｉｅｓｏｆｎｅｕｒａｌｎｅｔｗｏｒｋｍｏｄｅｌｈａｖｅｂｅｎｔｈｅｎｅｗｆｏｃｕｓｏｆｓｔｕｄｉｅｓｉｎｔｈｅｗｏｒｌｄ．Ｉｔｉｓｗｅｌ＿ｋｎｏｗｎｔｈａｔｑｕ...     

THE POSITIVE INVARIANT SET OF THE DIFFERENTIAL EQUATION ON BANACH SPACE

ＴｈｉｓｐａｐｅｒｇｉｖｅｓａｎｅｗｖｅｒｓｉｏｎｏｆａｔｈｅｏｒｅｍｏｆＭｉｔｉｏＮａｇｕｍｏ［３］，ｃｏｎｃｅｒｎｉｎｇｔｈｅｐｏｓｉｔｉｖｅｉｎｖａｒｉａｎｃｅｏｆａｓｅｔｗｉｔｈｒｅｓｐｅｃｔｔｏｔｈｅｄｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ（...     

DYNAMICAL BEHAVIORS FOR A THREE－DIMENSIONAL DIFFERENTIAL EQUATION IN CHEMICAL SYSTEM

ＤＹＮＡＭＩＣＡＬＢＥＨＡＶＩＯＲＳＦＯＲＡＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＩＮＣＨＥＭＩＣＡＬＳＹＳＴＥＭＬＩＮＹＩＰＩＮＧ（ＳｅｃｔｉｏｎｏｆＭａｔｈｅｍａｔｉｃｓ，ＫｕｎｍｉｎｇＩｎｓｔｉｔｕｔｅｏｆＴ...     

平面自治系统的规范型与闭轨族周期的临界点

本文通过平面复自治系统的规范型研究实系统具有可线性化的中心和鞍点的条件,定义了k-阶广义细中心及其判定量,给出了计算判定量的递推公式,并对三次系统,讨论了周期的临界点分枝问题.     

分支理论在高维生物模型中的应用

本文介绍分支理论和浑沌理论在高维生物模型中的应用,提供了许多可供研究的模型,是一篇较好的综述报告.     

一类时滞神经网络模型的稳定性

利用Ｌｙａｐｕｎｏｖ泛函,讨论了一类时滞神经网络模型ｕ′ｉ（ｔ）＝－ｂｉｕｉ（ｔ）＋∑ｎｊ＝１Ｔｉｊｆｊ（μｊｕｊ（ｔ－τｊ））＋ｃｉτｊ≥０,ｉ＝１,２,…,ｎ平衡态的稳定性,获得了几个充分条件     

GLOBAL BIFURCATIONS IN A PERTURBED CUBIC SYSTEM WITH Z_2-SYMMETRY

In this paper we consider global and local bifurcations in disturbed planar Hamiltonianvector fields which are invariant under a rotation over π. All calculation formulas of bifurcationcurves have been obtained. Various possible distributions and the existence of limit cycles andsingular cycles in different parameter regions have been determined. It is shown that for a planarcubic differential system there are infinitely many parameters in the three-parameter space suchthat Hilbert number H(3)≥11.     

Bifurcation of periodic solution in a three-unit neural network with delay

1. IntroductionDynamical characteristics of neural networks have become recelltly a subject of intenseresearch activity. J. B6lair and S. Dufou.[1] investigated a system of neural networks introduced by Hopfield[2]. Especially' they studied the three-uult network system with noself connectiondxi(t) 3dt = --xi(t) Z Ti,f; (x;(t -- T)), i = 1, 2, 3, (l)J = 1where f;(0) = 0, j = 1, 2, 3 and T, = 0, i = 1, 2, 3, give the stability properties of the nullsolution. [2] discussed the lineaJr stab…     

翻转的Varga材料球壳的渐近分支

众所周知,弹性球壳在翻转后可能不再保持球壳形状而出现起皱现象,也就是出现分支解。本文运用WKB方法,分析了各向同性且不可压缩的超弹性Varga材料球壳翻转后的变形问题。在大模数情形下,对于A-B=O(1),得到了球壳内、外径比的分支临界值的渐近表达式。对模数区域内几乎所有的模数,分析结果与数值结果吻合得很好。