Dynamical Systems Approach to Higher-level Heritability

To explain higher-level heritability, we propose a dynamical systems approach, based on simulations of the high-dimensional replicator equation with mutation dynamics. We assume that all variants are generated from within the groups of variants through mutations. Simulating the equation with a random interaction matrix and possible variants, we report that this system tends to have many attractors, of fixed point, chaotic and quasiperiodic type. In a chaotic attractor, special gene-like variants appear to control the heritability ofthe system, in the sense that removal of the variants would easily enable the system to depart from the attractor. Those variants do not predominate in thepopulation size, but have the lowest net reproduction and mutation rates on average. Because their rate of growth is small, they are named neutral phenotypes. Additionally, combinatorial effects of these neutral variants to the entire system are reported.     

Correlations in one-dimensional fully developed chaos

Correlations in the baker map and the tent map as examples of one-dimensional, fully developed chaos are considered. It is shown, utilizing symbolic dynamical systems derived from these maps, that the vanishing second-order correlation function is not sufficient to guarantee uncorrelatedness. Importance of the higher-order, especially third-order, correlation functions is emphasized for chaotic systems. In search of the quantities that grasp correlational behaviors as a whole in chaotic systems, it is proposed to use the fixed-separation correlation integral, which is a modified quantity of the usual correlation integral devised to calculate the fractal dimension of strange attractors, for these maps. It is shown that the new quantity contains all the even-number orders of autocorrelation function that are commonly considered.     

Wave separation versus bandpass filtering: a comparative non-linear analysis of brain α-EEG signals with and without psychotropic drug treatment

Attempts to demonstrate low-dimensional attractor behaviour in the analysis of electroencephalographic (EEG) signals meet with difficulties that in part stem from a departure from single-system dynamics. In order to address this problem, the -waves can be extracted by digital filtering or by wave separation; these two techniques are compared in order to specify the conditions in which finite impulse response (FIR) bandpass filters can be used. The comparison was made using 18 EEG records of 3 min duration under resting conditions (6 subjects, 3 records per subject: prior to apomorphine administration, then 90 min and 150 min post-treatment). No presence of low-dimensional dynamic episodes in -signals was observed without digital processing. Sixty 5 s sections showing attractor behaviour were found after filtering and twenty five 5 s sections after wave separation. The mean correlation dimension was calculated for each experimental condition and for 4 subjects, in order to observe the temporal profile of the drug. When attractors were found after wave separation, bandpass filtering then also showed attractor behaviour, with the same temporal profile. However, the reverse is not true: attractors were found after bandpass filtering that were not present after wave separation; in this case the results deserve confirmation, although the temporal profiles for all cases in which attractors were found after filtering remained comparable.     

Wave-separation in complex systems. Application to brain-signals

A departure from single-system dynamics, that may arise in characterizing self-organized dynamics of complex systems, is dealt with by using the Karhunen-Loève expansion of the trajectory matrix to decompose an experimental signal in a sum of spectral features. For an electroencephalographic -signal, a separation of waves and extraction of additive sub-signals are achieved, each sub-signal covering a well-bounded and physiologically meaningful frequency range. From the subsignals, an attractor that vanishes on phase-randomizing the data is characterized, under conditions where none was found for the recorded signal.     

生物实验数据的某些非线性分析方法

简要介绍常用的非线性动力学参量,结合生物学实验数据的特点,给出几种最新的分析方法.     

Global bifurcations of a periodically forced nonlinear oscillator

The effects of periodic pulsatile stimulation on a simple mathematical model of biological oscillations, called the radial isochron clock (RIC), are investigated as a function of stimulus frequency and amplitude. This system can be reduced to a two parameter, one-dimensional circle map. Numerical and topological methods are used to give a very detailed picture of the observed bifurcations over the complete range of parameters. The bifurcations are generic for a class of models which generalize the RIC.     

离散广义Logistic模型的稳定性和浑沌现象

文[1]提出了单种生长的连续性文广义Logistic dx/dt=γx({K-x}/(K+px))其中γ>ο为种群的内禀生长率,K>0为环境容纳量,ν>-1表示种群对环境(包括营     

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。     

生态复杂性研究——综述与展望

简要介绍了生态复杂性研究的最新进展与动态,生态复杂性研究的背景及若干重要的概念与方法,生态复杂性指生态系统内不同层次上的结构与功能的多样性,自组织及有序性,生态复杂性研究的显著特征是：它应用复杂的理论,方法和观点来研究生态与进化问题,其研究方法主要有元胞机法和遗传算法,认为生态系统是一个适应复杂系统,处于混沌的边缘或临界态,内部作用是生态系统复杂化,有序化及自组织的主要推动力。