腔内电光调制激光系统的混沌模拟

采用数值模拟的方法讨论了带反馈的腔內电光调制激光系统功率输出的分叉和混沌行为,得到了输出功率随控制参数变化的分叉图,和一些定量结果。     

连续时延神经网络的Hopf分岔现象研究

讨论了带连续时延神经网络的Hopf分岔现象。对于强核和弱核的情况,利用平均时延作为分岔参数,证明了模型经历了Hopf分岔过程。在带弱核的神经网络模型中,得到了分岔周期解稳定性准则。给出了一些数值例子,通过计算机仿真验证了所得结论的正确性。     

延迟决策对一类产出系统演化的影响研究

企业作为有限理性的经济主体,在做下阶段的生产决策时可能不仅考虑本期而是要综合考虑以往连续多期的边际利润情况。研究表明,加入时滞以后,系统纳什平衡点的稳定域明显扩大,从而为在混沌经济系统中实现倍周期分岔控制提供了现实途径,同时,还会使系统在纳什平衡点出现hopf分岔等新的动力学演化行为。而且,以累积利润为指标的系统表现可以得到改善。首先引入延迟决策的企业将获得更大的相对竞争优势。而在两家企业都引入延迟决策的情况下,伴随第二家企业产量调整速度的增加,它们将交替获得竞争优势。     

Pre‐procreative ages in population stability and cyclicity

Age‐specific models of population renewal (with and without feedback) which imply convergence to a stable state for some levels of fertility or feedback may imply the presence of long‐term cycling around a constant or exponentially changing equilibrium for other levels of fertility or feedback. The switch from one regime to the other is a “bifurcation.”; The conditions for bifurcation involve the roots of an analogue of Lotka's Equation.

Typically bifurcation is induced by raising the strength of feedback or the level of fertility. It has been known since the early 1980s, however, that this is sometimes impossible. It is sometimes impossible even with the linear renewal equation itself and with the most basic of non‐linear models, Lee's cohort feedback model.

Here it is proved that this typical route to bifurcation does not fail for these basic models in the presence of a condition which always holds for realistic applications with higher organisms: the existence of a span of ages before the onset of fertility.

Specifically, a strictly positive lower bound on ages of procreation is proved to be sufficient to guarantee the existence of a rescaling of Lotka's Equation for which the real part of some complex root vanishes. This result holds for absolutely Lebesgue‐integrable (signed) net maternity functions on the positive real line and for absolutely summable (signed) net maternities on the positive integers.

It follows that Coale's rescaling device for the analysis of approach to stability in stable population theory can be implemented for all realistic human net maternity schedules. It also follows that the many special cases of the cohort feedback model throughout population biology will all generate persistent cycling instead of stability if feedback is sufficiently strong.     

一类含有随机参数的混沌系统的Hopf分岔研究

文章选取随机变量为系统的随机变量研究含有随机参数混沌系统的Hopf分岔,利用Chebyshev正交多项式逼近理论将含有随机变量的系统转化为等价的确定性系统,通过Hopf分岔定理和Lyapunov系数讨论了随机参数系统的Hopf分岔及稳定性,发现随机系统的渐进稳定性参数区间大小不仅和确定性参数有关,还与随机参数有非常密切的关系.     

分支问题等价的一个充分条件

利用奇点理论的思想和方法研究了具有平凡解的分支问题．在t-等价群作用下,得到了具有平凡解的分支问题等价的充分条件．     

光学湍流中的滞后現象

本文以延时反馈光电混合型光学双稳装置为例,在先前他人工作的基础上,给出了下列光学湍流中的新的结果:在适当选择系统增益情况下,原有双稳区可能分裂为三个,以及延时算子的高阶影响,特别是在实验上首次观察到了分岔点的滞后现象.     

Bifurcation for a Type of Quasilinear Elliptic Equations On R" under the Natural Growth Conditions

The article proved the existence of H~1 (R) ∩ L~∞ (R~n) at the bifurcation λ= 0 by discussing the following nonlinear eigenvalue:—D-(ij)(a_(ij)(x,u)D_ju) +1/2a_(iju)(x,u)D_iuD_ju — q(x)|u|~σu = λu0≠u∈H~1(R~n) ,0<σ< 4/n,n≥3,x∈ R~nMeanwhile the article studied the conditions of q(x) under which λ=0 was a bifurcation point for the nonlinear eigenvalue . Here a_(ij) are not required to be bounded as u varies.     

低浓度三分子模型的振幅方程

首先在考虑扩散流随时间变化的基础上,建立了低浓度三分子模型的双曲型反应－扩散方程及其波动方程,然后运用奇异微扰理论导出在Ｈｏｐｆ分岔点处的小振幅方程,为研究系统的能量演化奠定了理论基础