Gait stability,variability and complexity on inclined surfaces

This study evaluated the gait stability, variability, and complexity of healthy young adults on inclined surfaces. A total of 49 individuals walked on a treadmill at their preferred speed for 4 min at inclinations of 6%, 8%, and 10% in upward (UP) and downward (DOWN) conditions, and in horizontal (0%) condition. Gait variability was assessed using average standard deviation trunk acceleration between strides (VAR), gait stability was assessed using margin of stability (MoS) and maximum Lyapunov exponent (λs), and gait complexity was assessed using sample entropy (SEn). Trunk variability (VAR) increased in the medial-lateral (ML), anterior-posterior, and vertical directions for all inclined conditions. The SEn values indicated that movement complexity decreased almost linearly from DOWN to UP conditions, reflecting changes in gait pattern with longer and slower steps as inclination increased. The DOWN conditions were associated with the highest variability and lowest stability in the MoS ML, but not in λs. Stability was lower in UP conditions, which exhibited the largest λs values. The overall results support the hypothesis that inclined surfaces decrease gait stability and alter gait variability, particularly in UP conditions.     

A deterministic analysis of self-incompatibility alleles

A number of plant species have a self-incompatibility locus that prevents self-fertilization. We 'analyse a deterministic model with an arbitrary number of alleles. We prove that the only polymorphic equilibrium is the one for which all (heterozygous) genotypes are equally frequent, and we prove that all (initially) polymorphic populations converge to this equilibrium.     

具收获与投放的三种群Volterra模型的周期轨道

本文在文〔2〕的基础上,研究三维动力系统的Lyapunov分枝问题．放宽了文〔2〕中关于向量场函数的限制,相应地给出从空间闭轨族扰动产生孤立周期解的判定方法．应用判定定理及椭圆函数的积分技巧,研究了具有收获与投放的三种群Volterra模型,得到了存在周期轨道的充分条件．     

Non-equilibrium thermodynamics of Lotka-Volterra ecosystems: Stability and evolution

A non-equilibrium thermodynamic theory of generalized Lotka-Volterra ecosystem has been presented. The main results consist of the derivation of a generalized expression of entropy-production for the evolutionary ecosystem and the study of its role in the analysis of ecological stability, succession and also in the formulation of some extremum principles characterising the evolution of the ecosystem.     

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。     

Viscoelastic creep induced by repetitive spine flexion and its relationship to dynamic spine stability

Repetitive trunk flexion elicits passive tissue creep, which has been hypothesized to compromise spine stability. The current investigation determined if increased spine flexion angle at the onset of flexion relaxation (FR) in the lumbar extensor musculature was associated with altered dynamic stability of spine kinematics. Twelve male participants performed 125 consecutive cycles of full forward trunk flexion. Spine kinematics and lumbar erector spinae (LES) electromyographic (EMG) activity were obtained throughout the repetitive trunk flexion trial. Dynamic stability was evaluated with maximum finite-time Lyapunov exponents over five sequential blocks of 25 cycles. Spine flexion angle at FR onset, and peak LES EMG activity were determined at baseline and every 25th cycle. Spine flexion angle at FR increased on average by 1.7° after baseline with significant increases of 1.7° and 2.4° at the 50th and 100th cycles. Maximum finite-time Lyapunov exponents demonstrated a transient, non-statistically significant, increase between cycles 26 and 50 followed by a recovery to baseline over the remainder of the repetitive trunk flexion cycles. Recovery of dynamic stability may be the consequence of increased active spine stiffness demonstrated by the non-significant increase in peak LES EMG that occurred as the repetitive trunk flexion progressed.     

Global dynamics of two-compartment models for cell production systems with regulatory mechanisms

We present a global stability analysis of two-compartment models of a hierarchical cell production system with a nonlinear regulatory feedback loop. The models describe cell differentiation processes with the stem cell division rate or the self-renewal fraction regulated by the number of mature cells. The two-compartment systems constitute a basic version of the multicompartment models proposed recently by Marciniak-Czochra and collaborators [25] to investigate the dynamics of the hematopoietic system. Using global stability analysis, we compare different regulatory mechanisms. For both models, we show that there exists a unique positive equilibrium that is globally asymptotically stable if and only if the respective reproduction numbers exceed one. The proof is based on constructing Lyapunov functions, which are appropriate to handle the specific nonlinearities of the model. Additionally, we propose a new model to test biological hypothesis on the regulation of the fraction of differentiating cells. We show that such regulatory mechanism is incapable of maintaining homeostasis and leads to unbounded cell growth. Potential biological implications are discussed.