Partial and complete periodic synchronization in coupled discontinuous map lattices

The partial and complete periodic synchronization in coupled discontinuous map lattices consisting of both discontinuous and non-invertible maps are discussed. We classify three typical types of periodic synchronization states, which give rise to different spatiotemporal patterns including static partial periodic synchronization, dynamically periodic synchronization, and complete periodic synchronization patterns. A special prelude dynamics of partial and complete periodic synchronization motion, which is shown by five separated concave curves in the time series plots of the order parameters,is observed. The detailed analysis shows that the special prelude dynamics is induced by the competition between two synchronized clusters, and the analytical expression for the corresponding order parameter is obtained.     

浑沌信号在数据加密中的应用

根据非线性系统的特点和浑沌同步原理，我们提出了一种新的数据加／解密方法，并将此方法应用于对全文数据和数据库中部分字段的加／解密工作中，结果表明，这种加／解密方法的算法简单，钥匙多样复杂，较传统加解密方法更难进行解密，具有一定的推广应用价值。     

Noise destroys the coexistence of periodic orbits of a piecewise linear map

The effects of Gaussian white noise and Gaussian colored noise on the periodic orbits of period-5(P-5) and period-6(P-6) in their coexisting domain of a piecewise linear map are investigated numerically.The probability densities of some orbits are calculated.When the noise intensity is D = 0.0001,only the orbits of P-5 exist,and the coexisting phenomenon is destroyed.On the other hand,the self-correlation time τ of the colored noise also affects the coexisting phenomenon.When τcττc,only the orbits of P-5 appear,and the stability of the orbits of P-5 is enhanced.However,when ττc(τc and τc are critical values),only the orbits of P-6 exist,and the stability of the P-6 orbits is enhanced greatly.When ττc,the orbits of P-5 and P-6 coexist,but the stability of the P-5 orbits is enhanced and that of P-6 is weakened with τ increasing.     

Interpreting a period-adding bifurcation scenario in neural bursting patterns using border-collision bifurcation in a discontinuous map of a slow control variable

<正>To further identify the dynamics of the period-adding bifurcation scenarios observed in both biological experiment and simulations with the differential Chay model,this paper fits a discontinuous map of a slow control variable of the Chay model based on simulation results.The procedure of period adding bifurcation scenario from period k to period k + 1 bursting(k = 1,2,3,4) involved in the period-adding cascades and the stochastic effect of noise near each bifurcation point is also reproduced in the discontinuous map.Moreover,dynamics of the border-collision bifurcation are identified in the discontinuous map,which is employed to understand the experimentally observed period increment sequence.The simple discontinuous map is of practical importance in the modeling of collective behaviours of neural populations like synchronization in large neural circuits.     

Intermittent Chaotic Neural Firing Characterized by Non-Smooth Features

A chaotic firing pattern, characterized by non-smooth features and generated through the routine of intermittency from period 3, is observed in biological experiments on a neural firing pacemaker and reproduced in simulations by using a theoretical neuronal model with multiple time scales. This chaotic activity exhibits a scale law very similar to those of both the type-Ⅰ intermitteney generated in smooth systems and the type-Ⅴ intermittency in non-smooth systems.     

一个不连续映象中的混沌稳定或混沌抑制

借助于一个张弛振子模型和与之相应的不连续映象说明了在这类系统中瞬态集的映蔽效应会产生三种区域：1）稳定混沌区，在此区域中不存在周期窗口，混沌轨道是结构稳定的；2）完全锁相区，在此区域中混沌被抑制，只存在周期运动；3）准周期区域，在此区域中混沌被抑制，只存在准周期或临界稳定的周期运动．这种思想被用来解释在一个实际张弛振子电路中观察到的稳定混沌区和完全锁相区 关键词：     

动力学不连续性引起的新型激变

在描述张弛振子的一维不连续映象中，可以观察到由于混沌吸引子与动力学不连续点集碰撞而引起的具有新特征的激变．参量空间中的表征不同特征激变的四个临界曲面有可能会聚于一个公共“尖点”．在此尖点附近，参量的扰动会导致混沌吸引子的突然膨胀或收缩 关键词：     

度关联无标度网络上的有倾向随机行走

有倾向随机行走是研究网络上数据包路由策略的有效方法. 由于许多真实技术网络包括互联网都具有负的度关联特征, 因此本文研究这种网络上的有倾向随机行走性质. 研究表明: 在负关联网络上粒子可以在连接度较大的节点上均匀分布, 而连接度小的节点上粒子较少; 负关联网络上随机行走的速度比非关联网络更快; 找到了负关联网络上的最佳倾向性系数, 在此情况下负关联网络上随机行走的速度远快于非关联网络. 负关联网络既可以利用度小的节点容纳粒子, 又可以利用度大的节点快速传输, 这是负关联网络上高行走效率产生的机制.     

非晶铁中位形熵与信息维的压力响应

本文分析了非晶铁模型中原子能量分布的信息维和位形熵随压力的变化。计算了原子相互作用能的粒子数分布,将其分布的信息维作为非晶态位形熵的度量。计算结果表明,原子能量分布曲线和位形熵与统计时所取能量间隔有关;位形熵与能量间隔之间具有分形标度关系。用介于由能量间隔的下截止限和上截止限所确定的无标度区内的平均值表示各压力下的位形熵。模拟结果表明,原子能量分布的信息维是描述非晶系统无序状态的另一有效参量;压力对非晶金属结构无序及分维值的影响呈较复杂的波动变化趋势。 关键词：     

一个全局耦合不连续映像格子中的奇异态

文章研究了一类由既不可逆又不连续映像构成的全局耦合映像格子系统中的奇异态行为,计算了系统的同步序参量和空间振幅变化图.结果表明,在某些特定的参数区间内,耦合映像格子系统会出现奇异态或团簇态,并且敏感地依赖于耦合强度的选择.上述丰富的动力学现象是由于单映像中不连续、不可逆性以及空间耦合相互作用的结果.通过数值模拟找到了奇异态或团簇态出现的特定参数区域.