Dynamics of the logistic map under discrete parametric perturbation

By introducing a periodic perturbation in the control parameter of the logistic map we have investigated the period locking properties of the map. The map then gets locked onto the periodicity of the perturbation for a wide range of values of the parameter and hence can lead to a control of the chaotic regime. This parametrically perturbed map exhibits many other interesting features like the presence of bubble structures, repeated reappearance of periodic cycles beyond the chaotic regime, dependence of the escape parameter on the seed value and also on the initial phase of the perturbation etc.     

SEDIMENTARY CHARACTERISTICS AND BASINAL EVOLUTION OF XIZANG (TIBET) TETHYS IN MESOZOIC ERA

Based on the characteristics of stratigraphy sedimentary system and paleotectonics, Xizang (Tibet) Tethys can be classified into nine sedimentary basins. The sedimentary and development characteristics of each basin nicely reveal the plate tectonic framework of Xizang (Tibet). The studies show that the Bangong Lake-Dengen fracture zone is intraplate transform boundary, the active continental margin of the Yarlung Zangbo River is of the nature of "range-arc" boundary, not trench-arc-back-arc basin system.     

Optimal control of sea level in a tidal basin by means of the Pontryagin maximum principle

The maximum principle has been applied in optimizing the sea level, induced by a tidal component, in a small basin. The water level control has been simulated by means of gate operations acting at the open mouth of the tidal basin. The main feature of the model is that the control operations do not require complete closure of the basin but only a variable reduction of its mouth. Although the equations describing the dynamics of the basin have been simplified, the results obtained are expected to be of practical use.     

随机激励对软弹簧杜芬振子动力学的分散作用

讨论了有界噪声激励对软弹簧杜芬振子的倍周期分岔至混沌运动的影响。利用蒙特卡罗方法,通过对系统受侵蚀安全盆的变化状况进行了观察,并由此对后继动力学分析的初始点进行了选取。系统的相图、倍周期分岔图以及庞加莱映射图等方面的数值结果表明,外加随机激励的作用往往掩盖原确定性系统内在的规则运动,对原确定性系统的运动具有较典型的分散作用,可延缓系统的倍周期分岔,也可使得系统内在随机行为提前发生,即可使得系统更容易出现混沌运动。     

Optimal Control of Nonregular Dynamics in a Duffing Oscillator

A method for controlling nonlinear dynamics and chaos previouslydeveloped by the authors is applied to the classical Duffing oscillator.The method, which consists in choosing the best shape of externalperiodic excitations permitting to avoid the transverse intersection ofthe stable and unstable manifolds of the hilltop saddle, is firstillustrated and then applied by using the Melnikov method foranalytically detecting homoclinic bifurcations. Attention is focused onoptimal excitations with a finite number of superharmonics, because theyare theoretically performant and easy to reproduce. Extensive numericalinvestigations aimed at confirming the theoretical predictions andchecking the effectiveness of the method are performed. In particular,the elimination of the homoclinic tangency and the regularization offractal basins of attraction are numerically verified. The reduction ofthe erosion of the basins of attraction is also investigated in detail,and the paper ends with a study of the effects of control on delayingcross-well chaotic attractors.     

Chaotic Saddles in Wada Basin Boundaries and Their Bifurcations by the Generalized Cell-Mapping Digraph (GCMD) Method

By means of the generalized cell-mapping digraph (GCMD) method, we studybifurcations governing the escape of periodically forced oscillatorsfrom a potential well, in which a chaotic saddle plays an extremelyimportant role. In this paper, we find the chaotic saddle anddemonstrate that it is embedded in a strange fractalbasin boundary which has the Wada property that any point that is on theboundary of that basin is also simultaneously on the boundary of atleast two other basins. The chaotic saddle in the Wada basin boundary,by colliding with a chaotic attractor, leads to a chaotic boundarycrisis with indeterminate outcome. A local saddle-node fold bifurcation,if the saddle of the saddle-node fold is located in tangency with thechaotic saddle in the Wada basin boundary, also results in a strangeglobal phenomenon, namely that the local saddle-node fold bifurcation hasglobally indeterminate outcome. We also investigate the origin andevolution of the chaotic saddle in the Wada basin boundary, particularlyconcentrating on its discontinuous bifurcations (metamorphoses). Wedemonstrate that the chaotic saddle in the Wada basin boundary iscreated by a collision between two chaotic saddles in differentfractal basin boundaries. After a final escape bifurcation, there onlyexists the attractor at infinity and a chaotic saddle with a beautifulpattern is left behind in the phase space.     

Nonlinear oscillations and chaotic motions in a road vehicle system with driver steering control

The nonlinear dynamics of a differential system describing the motion of a vehicle driven by a pilot is examined. In a first step, the stability of the system near the critical speed is analyzed by the bifurcation method in order to characterize its behavior after a loss of stability. It is shown that a Hopf bifurcation takes place, the stability of limit cycles depending mainly on the vehicle and pilot model parameters. In a second step, the front wheels of the vehicle are assumed to be subjected to a periodic disturbance. Chaotic and hyperchaotic motions are found to occur for some range of the speed parameter. Numerical simulations, such as bifurcation diagrams, Poincaré maps, Fourier spectrums, projection of trajectories, and Lyapunov exponents are used to establish the existence of chaotic attractors. Multiple attractors may coexist for some values of the speed, and basins of attraction for such attractors are shown to have fractal geometries.     

Fractal basin boundaries in a two-degree-of-freedom nonlinear system

The final state for nonlinear systems with multiple attractors may become unpredictable as a result of homoclinic or heteroclinic bifurcations. The fractal basin boundaries due to such bifurcations for a four-well, two-degree-of-freedom, nonlinear oscillator under sinusoidal forcing have been studied, based on a theory of homoclinic bifurcation inn-dimensional vector space developed by Palmer. Numerical simulation is used as a means of demonstrating the consequences of the system dynamics when the bifurcations occur, and it is shown that the basin boundaries in the configuration space (x, y) become fractal near the critical value of the heteroclinic bifurcations.     

Wada分形吸引域边界上的混沌鞍

应用广义胞映射图论（Generalized Cell Mapping Digraph)方法，数值地研究Thompson的逃逸方程在最佳逃逸点附近的分岔。发现了嵌入在Wada分形吸引域边界上的混沌鞍，混沌鞍是状态空间不稳定（非吸引）的混沌不变集合。Wada分形吸引域边界是具有Wada性质的边界，即吸引域边界上的任意点也同时是至少两个其它吸引域的边界点，称为Wada域边界。我们证明Wada域边界上的混沌鞍导致局部鞍结分岔具有全局不确定性结局，研究了Wada域边界上混沌鞍的形成与演化，证明最终的逃逸分岔是混沌吸引子碰撞混沌鞍的边界激变。     

陇西盆地段黄河发育时代问题的新认识

根据陇西盆地的两个次级盆地阶地即兰州盆地最高级黄河阶地和陇西盆地黄河一级支流大夏河最高级阶地的磁性地层学研究表明,二者的形成时代大致相同,约为１．６ＭａＢ．Ｐ．左右,也即此时黄河才开始在这两个盆地中出现．这一结果修订了黄河在陇西盆地中出现的最早时间．完整的黄河阶地系列实际上是第四纪期间青藏高原阶段性隆升的忠实记录．