Stability on finite time interval and time-dependent bifurcation analysis of Duffing's equations

The concept of stability on finite time interval is proposed and some stability theorems are established. The delayed bifurcation transition of Dufflng's equations with a time-dependent parameter is analyzed. Function is used to predict the bifurcation transition value. The sensitivity of the solutions to initial values and parameters is also studied.     

IUTAM“面向先进技术与工程设计的非线性动力学会议”概况

<正>2010年7月27日～30日,由国际理论与应用力学联合会(IUTAM)主办的"面向先进技术与工程设计的非线性动力学会议"在英国阿伯丁召开.会议由英国阿伯丁大学工学院M.Wiercigroch教授和意大利罗马大学工学院G.Rega教授担任主席,来自英国、德国、法国、意大利、荷兰、奥地利、西班牙、葡萄牙、丹麦、波兰、俄罗斯、乌克兰、以色列、中国、日本、印度、美国、加拿大和巴西等19个国家的75名学者出席了会议,52位学者做了学术报告,17位学者做了墙报交流.     

Nonlinear dynamics and vibration reduction of a dry friction oscillator with SMA restraints

The dynamic behaviors of a dry friction oscillator with shape memory alloy (SMA) are investigated. Motion equations of the system are formulated by the restoring force of the oscillator in terms of a polynomial constitutive model dependent mainly on the temperature. The vibration response of the system and the influence of the temperature are investigated. It is shown that chaotic motions can be observed and dramatically changed by temperature characteristics. Moreover, some sliding bifurcations are also discovered and influenced by the temperature. Compared with conventional dry friction elastic oscillators, the dry friction SMA oscillator presents much richer dynamic behavior caused by pseudo-elasticity, and vibration reduction can be achieved through the shape memory property of SMA restraints.     

A station-keeping strategy for collinear libration point orbits

Spacecrafts in periodic or quasi-periodic orbits near the collinear libration points are proved to be excellent platforms for scientific investigations of various phenomena. Since such periodic or quasi-periodic orbits are exponentially unstable, the station-keeping maneuver is needed. A station-keeping strategy which is found by an analytical method is presented to eradicate the dominant unstable component of the libration point trajectories. The inhibit force transforms the unstable component to a stable component. In this method, it is not necessary to determine a nominal orbit as a reference path.     

非自治时滞反馈控制系统的周期解分岔和混沌

研究时滞反馈控制对具有周期外激励非线性系统复杂性的影响机理, 研究对应的线性平衡态失稳的临界边界, 将时滞非线性控制方程化为泛函微分方程, 给出由Hopf分岔产生的周期解的解析形式. 通过分析周期解的稳定性得到周期解的失稳区域, 使用数值分析观察到时滞在该区域可以导致系统出现倍周期运动、锁相运动、概周期运动和混沌运动以及两条通向混沌的道路: 倍周期分岔和环面破裂. 其结果表明, 时滞在控制系统中可以作为控制和产生系统的复杂运动的控制``开关'.     

一类时变动力系统的高余维分岔及其控制

研究了一类时变动力系统的高余维分岔及其控制问题,首先利用新方法对时变分岔方程的两个方向的分岔转迁和跃迁现象进行分析,分别通过慢变解的线性化近似和量级平衡估计分岔转迁值,然后研究这类时变分岔方程的线性反蚀控制问题,通过分析相应的二维高次自治系统的Hopf分岔,在适当的条件下得到了稳定的动态滞后环,研究揭示出脉冲振动产生的机理是分岔参数随时间周期变化经过定常分岔值时所发生的分岔转迁的滞后和跃迁现象。     

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为了更好地发挥<力学进展>对力学研究的促进作用,编委会决定,选择有发展前景的若干力学研究方向组织专辑评述:即,每次围绕一个方向约请若干国内外知名专家从不同的角度撰写综述评论文章,集中于一期内发表,并提供较详细的重要参考文献,以便向读者展示该方向最新发展的全貌,从而达到开阔学术思想、启发探索兴趣、提供研究导向的目的.     

Codimension-two bifurcation analysis on firing activities in Chay neuron model

Using codimension-two bifurcation analysis in the Chay neuron model, the relationship between the electric activities and the parameters of neurons is revealed. The whole parameter space is divided into two parts, that is, the firing and silence regions of neurons. It is found that the transition sets between firing and silence regions are composed of the Hopf bifurcation curves of equilibrium states and the saddle-node bifurcation curves of limit cycles, with some codimension-two bifurcation points. The transitions from silence to firing in neurons are due to the Hopf bifurcation or the fold limit cycle bifurcation, but the codimension-two singularities lead to complexity in dynamical behaviour of neuronal firing.