EEG动力学模型中混沌现象的研究

通过对脑电图（electroencephalogram,EEG）动力学模型模拟出的EEG信号的相图、分岔图、功率谱、关联维数和Lyapunov指数的对比研究,得出如下结论：1）该模型是按周期行为与混沌现象交替出现的间歇突发通向混沌的,且该间歇性与Hopf分岔、倍周期分岔和逆分岔有关;2）支持了EEG中存在混沌运动的观点。     

基于混沌理论的蛋白质序列特性的研究

蛋白质序列特性的研究对于蛋白质的结构及功能具有重要意义。该文为了研究蛋白质序列是否具有混沌行为,先将蛋白质序列通过氨基酸电子离子相互作用势(electron interaction potential,EIIP)转化为时间序列,再根据混沌理论对其进行相空间重构,利用去偏自相关系数,经典G-P算法确定系统的时间延迟t和嵌入维数m,系统的最大Lyapunov指数则用改进的最大Lyapunov指数计算方法计算,其结果绝大多数为正,从而确认了蛋白质时间序列的混沌行为,并对特例进行了说明。     

基于关联维数和Lyapunov指数高频脑电非线性动力学研究

目的:探讨利用非线性动力学理论特征值来区分老年人和青年人脑电的差异。方法:采用非线性动力学的关联维数和lyapunov指数对老年组和青年组的安静闭眼、安静睁眼和N-back字母记忆事件等的高频脑电进行特征提取,对特征值进行统计分析,分析两组特征值之间的差别。结果:安静闭眼和安静睁眼事件下,老年组多数导联的关联维数和lyapunov指数的特征值与青年组的特征值存在显著差异(P均0.05);N-back字母记忆事件下,老人多数导联的关联维数特征值大于青年的特征值,但老年组只有14导联的lyapunov指数特征值大于青年组的特征值(P均0.05)。不管有无思维活动,人脑在矢状线上的五个导联Fz、FCz、Cz、CPz、Pz的关联维数和lyapunov指数的特征值都处在峰值处。结论:老年人相比青年人脑功能弱、能量发放少;在思维活动情况下,老年需要更多地发放能量来完成相同的思维活动。安静闭眼和睁眼以及N-back字母记忆事件等三个事件的关联维数和lyapunov指数特征值可用来区分老年组和青年组脑电的差异。     

胃电的非线性动力学分析

我们用非线性动力学的方法分析了两例健康人的胃电图（Ｅｌｅｃｔｒｏｇａｓｔｒｏｇｒａｍ,简称ＥＧＧ）,得出它的功率谱、计算了它的关联维数和最大Ｌｙａｐｕｎｏｖ指数。结果显示：它的功率谱为一有尖峰的连续谱;其关联维数介于６和７之间;它的最大Ｌｖａａｕｎｏｖ指数大于０。由此,我们可以初步推知ＥＧＧ不是随机噪声,它服从确定性的动力学规律。     

蛋白质序列混沌特性的研究

为了研究蛋白质序列的特性,首先采用非线性预测方法,得到蛋白质序列的总体误差平均值图。并通过与随机序列,混沌序列的总体误差平均值图相比较,发现蛋白质序列有别于随机序列,和混沌序列很相似,则猜测蛋白质序列具有混沌特性。为了验证该猜测,将蛋白质序列通过混沌随机游走描述方法转化为时间序列,并计算其最大Lyapunov指数。在选取的时间延迟和嵌入维数下,每类蛋白质序列的最大Lyapunov指数都大于零,从而得出蛋白质序列具有混沌特性的结论。     

河流着生藻类多样性对城镇化的响应——以深圳市为例

着生藻类是河流生态状况的重要指示生物,然而关于城镇化对着生藻类多样性影响的研究还较缺乏。基于深圳市9条主要河流74个样点2020年雨、旱季的调查数据,对比了城区、郊区河流样点的着生藻类α、β多样性。两次调查共鉴定出着生藻类301个分类单元,其中硅藻门种类最多。谷皮菱形藻(Nitzschia palea)、隐头舟形藻(Navicula cryptocephala)、平庸菱形藻(Nitzschia inconspicua)等污染指示种在城区组相对丰度更高,而清洁指示种微小曲丝藻(Achnanthidium minutissimum)在郊区组相对丰度更高。城镇化对着生藻类物种丰富度、香农维纳多样性指数、Pielou均匀度指数等α多样性指数均无显著影响,但对着生藻类群落结构有显著影响。城区组样点的着生藻类β多样性(用主坐标分析质心指示)低于郊区组,城区组与郊区组藻类β多样性差异在旱季更为显著。两组样点的藻类β多样性差异主要来源于物种周转组分。与城区组着生藻类群落显著相关的环境因子包括总氮、高锰酸钾指数、电导率、pH、浊度和水深,而与郊区组着生藻类群落显著相关的是总氮、溶解性无机磷和电导率。研究...     

海岸线与海岸景观格局对人为干扰度的动态响应——以营口市南部海岸为例

利用多期遥感数据,提取营口南部海岸五期岸线变化信息、分维值,并利用Arcgis10.2中渔网工具创建评价单元。计算景观格局指数,构建人为干扰强度指标,并进一步探讨岸线变化和景观格局变化对人类活动的动态响应。结果表明:(1)研究区围垦导致岸线长度增长、岸线分形维数的增大,1990—2015年四个时段中岸线年增长速率为0.52%、0.53%、4.98%和0.96%;(2)景观格局指数反映2005年之前景观边界、形状复杂程度与破碎程度有所增加;2005年之后景观形状趋于规则化、土地利用趋于均衡化;(3)研究期间强干扰和弱干扰区域面积均有所增加,中等干扰强度区域面积减小;(4)斑块密度、总边缘长度、边缘密度、景观形状指数和平均分维值均与平均干扰强度指数变化同步。Shannon多样性指数与人为干扰强度变化呈反相关;(5)岸线长度变化和岸线分形维数变化都与人类干扰度呈反相关,相关性分别为-0.97和-0.98。     

森林景观变化的地理环境因素整合分析——以伊洛河流域洛宁县为例

运用景观生态学的基本原理,借助于地理信息系统技术,整合分析了地理环境因素对伊洛河流域洛宁县森林景观动态变化的影响。结果显示,应用地理环境因素影响指数可以很好地从整体上分析地理环境因素,如高程、坡度、距离居民点中心的距离、与森林边缘距离等地理环境因子对区域森林景观动态变化的影响。1983和1999年,伊洛河流域洛宁县森林景观在地理环境因素影响指数上的优势分布区间(Pie1)分别为1230和1030,即在中高地理环境因素影响指数分布区间内,且有向低地理环境因素影响指数分布区间略为移动的趋势。森林景观类型保持不变部分、森林景观转化为非森林景观类型部分和非森林景观转化为森林景观类型部分所对应的在地理环境因素影响指数上的优势分布区间(Pie1)分别为1130、18和613。通过建立森林景观动态变化与地理环境因素影响指数的相互关系,表明森林景观动态变化与地理环境因素影响指数(特别是在地理环境因素影响指数的优势分布区间内)有显著相关关系。     

长江三角洲地区全新世蕨类孢子与藻类——以奉贤DY03钻孔的产出类型为例

长江三角洲奉贤DY03钻孔的全新统沉积物中蕨类孢子和藻类的种类丰富,如何正确鉴别,并解释它们的来源、传播与沉积过程等问题,成为讨论过去生物多样性变化、古生态环境与气候事件的重要基础.本文收录奉贤DY03钻孔沉积物中出现频率较高的蕨类孢子和藻类,蕨类孢子可能鉴定到种或属的水平,但也有部分种类只能鉴定到科的水平,有的类型难以确定,则以形态种来归类.凤尾蕨科的种类具有突出的多样性(约8种类型),其次是水龙骨科、卷柏科、里白科、石松科,再次是紫萁科、水蕨科、桫椤科等.藻类根据生态型分为淡水域和咸水域或半咸水域的种类,前者以环纹藻和盘星藻为代表,后者则以沟鞭藻为典型.本研究包含的41种孢子和5种藻类可作为亚热带地区类似沉积环境的孢粉鉴定参考.文中还简要讨论了DY03钻孔的蕨类孢子来源和藻类的古生态学价值.     

基于样方数据的云南松林分生长模型研究——以云南省保山市杨柳白族彝族乡为例

以云南省保山市杨柳白族彝族乡实地调查的86块云南松样地数据,使用非线性拟合的方法拟合优选常用树木生长方程,建立了包括地位指数、密度指数、平均直径和蓄积量的生长模型。经验生长方程Schumacher的拟合度与其它方程相近,但模型中参数变异系数均比其余方程低,为地位指数、平均直径和蓄积量的最优方程。     

An analysis of the reliability phenomenon in the FitzHugh-Nagumo model

The reliability of single neurons on realistic stimuli has been experimentally confirmed in a wide variety of animal preparations. We present a theoretical study of the reliability phenomenon in the FitzHugh-Nagumo model on white Gaussian stimulation. The analysis of the model's dynamics is performed in three regimes—the excitable, bistable, and oscillatory ones. We use tools from the random dynamical systems theory, such as the pullbacks and the estimation of the Lyapunov exponents and rotation number. The results show that for most stimulus intensities, trajectories converge to a single stochastic equilibrium point, and the leading Lyapunov exponent is negative. Consequently, in these regimes the discharge times are reliable in the sense that repeated presentation of the same aperiodic input segment evokes similar firing times after some transient time. Surprisingly, for a certain range of stimulus intensities, unreliable firing is observed due to the onset of stochastic chaos, as indicated by the estimated positive leading Lyapunov exponents. For this range of stimulus intensities, stochastic chaos occurs in the bistable regime and also expands in adjacent parts of the excitable and oscillating regimes. The obtained results are valuable in the explanation of experimental observations concerning the reliability of neurons stimulated with broad-band Gaussian inputs. They reveal two distinct neuronal response types. In the regime where the first Lyapunov has negative values, such inputs eventually lead neurons to reliable firing, and this suggests that any observed variance of firing times in reliability experiments is mainly due to internal noise. In the regime with positive Lyapunov exponents, the source of unreliable firing is stochastic chaos, a novel phenomenon in the reliability literature, whose origin and function need further investigation.     

Chaotic dynamics of the surface potential of human skeletal muscles determined in electromyography

A new method for differential evaluation of electromyographic data on straited muscles of human lower extremities was developed. This method is based on nonlinear dynamics and thermodynamics and can be used for identification of pathologies. The distance between two trajectories of the potential of two symmetric muscles was the main measured characteristic of coordinated muscle work. These data were used to determine the Lyapunov exponent and the time of forgetting initial conditions, which reflect the generally chaotic dynamics of muscle activity. Application of the theory of deterministic chaos to analysis of electromyographic patterns can improve the diagnosis of peripheral nervous system diseases and the efficacy of treatment control. Quantitation of nonlinear dynamic parameters of muscle activity, clear data representation, high prognostic information content of the Lyapunov exponent and Kolmogorov entropy are among the advantages of the new method.     

Kinematic Analysis of the Neck and Upper Extremities During Walking in Healthy Young Adults

The objective of this paper is to quantify the local stabilities of the neck and upper extremities (right/left shoulders and right/left elbows), and investigate differences between linear and nonlinear measurements of the associated joint motions and differences in the local stability between the upper and lower extremities. This attempt involves the calculation of a nonlinear parameter, Lyapunov Exponent (LE), and a linear parameter, Range of Motion (ROM), during treadmill walking in conjunction with a large population of healthy subjects. Joint motions of subjects were captured using a three-dimensional motion-capture system. Then mathematical chaos theory and the Rosenstein algorithm were employed to calculate LE of joints as the extent of logarithmic divergence between the neighboring state-space trajectories of flexion-extension angles. LEs computed over twenty males and twenty females were 0.037±0.023 for the neck, 0.043±0.021 for the right shoulder, 0.045±0.030 for the left shoulder, 0.032±0.021 for the right elbow, and 0.034±0.026 for the left elbow. Although statistically significant difference in the ROM was observed between all pairs of the neck and upper extremity joints, differences in the LE between all pairs of the joints as well as between males and females were not statistically significant. Between the upper and lower extremities, LEs of the neck, shoulder, and elbow were significantly smaller than those of the hip (∼0.064) and the knee (∼0.062). These results indicate that a statistical difference in the local stability between the upper extremity joints is not significant. However, the different result between the ROM and LE gives a strong rationale for applying both linear and nonlinear tools together to the evaluation of joint movement. The LEs of the joints calculated from a large population of healthy subjects could provide normative values for the associated joints and can be used to evaluate the recovery progress of patients with joint related diseases.     

低维非线性呼吸系统的复杂性计算

首先应用混沌计算方法：关联维数D2和最大李亚普努夫指数LLE,以及替代数据分析法,分析了男性受试者在平静状态下记录的呼吸系统时间序列的混沌特征。同时,在呼吸变量的非线性分析中首次引进了被称为C0复杂度的新技术．它的应用将有助于更好地理解自主神经系统中潜在的生理过程。LLE计算的替代数据法分析结果显示,没有明确的证据可以证实受试者在平静状态下的呼吸时序的模态是混沌的。然而,C0复杂度的计算结果却表明大部分呼吸系统的时间序列表现为某种程度的复杂性,这为呼吸模态的非随机变化的属性提供了部分的实验和计算证据。更进一步,C0复杂度有可能以一种新的、确定的方式给出呼吸系统在激励状态下的量化改变。     

具有共生作用两种群离散耦合Logistic模型混沌控制

针对具有共生作用的离散耦合Logistic模型,首先采用Lyapunov指数方法验证了混沌现象的存在.然后详细地分析了系统随参数变化的分岔图,发现了系统中存在更复杂的现象.最后应用混沌跟踪控制方法控制系统的混沌现象,使得种群稳定到正不动点轨道上,消除了种群中存在的混沌现象.仿真结果验证了控制方法的有效性.     

脑干内的混沌

对脑干听觉诱发电位进行了非线性动力学分析,计算了关联维数Ｄ２和最大Ｌｙａｐｕｎｏｖ特征指数,确认ＢＡＥＰ是一个来源于低维混沌动力系统的时间序列,从而证明人类脑干存在着混沌现象,利用满足最小互信息标准的最佳延迟重构了二维混沌吸引子。