A centrosymmetric chaos

Symmetry plays an important part in the research of the dynamical behavior of nonlinear system. It is proved in this paper that, for a class of centrosymmetric systems with parametric excitation, chaos behaves in centrosymmetric manner, which implies that chaos need not to be an unsymmetric dynamical state. The project supported by National Natural Science Foundation of China     

AN EXAMPLE OF PDE WITH TWO ATTRACTORS

ＡＮＥＸＡＭＰＬＥＯＦＰＤＥＷＩＴＨＴＷＯＡＴＴＲＡＣＴＯＲＳＷａｎｇＧｕａｎｘｉａｎｇ（王冠香）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｕｚｈｏｕＵｎｉｖｅｒｓｉｔｙ，Ｓｕｚｈｏｕ２１５００６Ｐ．Ｒ．Ｃｈｉｎａ）ＸｕＺｈｅｎｙｕａｎ（徐...     

Sine-Gordon方程中混沌跳跃行为的机制

定性研究了Sine-Gordon方程在其广义近似惯性流形上的一个四维常微分方程。通过奇异扰动理论得到Silnikov同宿轨道存在的一个解析判定，然而在以往数值模拟中使用过的参数条件下，上面的判定不完全成立。于是进一步利用能量差方法，在这些参数条件下证明了至少存在四条结构稳定的脉冲轨道，它们正好反映了在Sine-Gordon方程的数值模拟中观察到 的混沌跳跃行为。     

AN IMPROVEMENT AND PROOF OF OGY METHOD

I.IntroductionRecenhycontrollingchaosbecomesaninterestingsubject.In1990,E.Ott,C.GreogiandJ.A.Yorkelllgaveacollceptionofcontrollingchaos,andgaveacontrollingmethodknownasOGYmethod.ThereweremanyresultsthatshowedOGYmethodiseffective.AfterOGY,manymethodsofcontrollingchaosweregiven,mostofthemwerebasedonOGY13'4'5'6'71.SoOGYmethodisthefundamentofcontrollingchaos.ToachieveaproofofOGYisanimportanttaskformathematicstheoryofcontrollingchaos.Thispaperchangesthemethodofchoosingparameter,andprove…     

WAVELET BASIS ANALYSIS IN PERTURBEDPERIODIC KdV EQUATION

I.IntroductionandSignsThephenomenaofnaturealwaysoccursatacertaintimeandacertainspace.Thecomplexityoftimeandspaceisduetodescribingtherelationbetweentimeandspaceandthelongtimebehaviorofsystembyusingthepartialdifferentialequation.Traditionally,thestatefunctionisexpandedinFotlrierseries,andthepartialdifferentialequationistransformedintotheordinarydifIYrentialequationwiththeevolutionofFouriercoefficientastimegoeson.ButitisverydifficulttoknowwelltheFouriercoefficientwhichplaysanimportantroleasthe…     

Emergence of modularity and disassortativity in protein-protein interaction networks

In this paper, we present a simple evolution model of protein-protein interaction networks by introducing a rule of small-preference duplication of a node, meaning that the probability of a node chosen to duplicate is inversely proportional to its degree, and subsequent divergence plus nonuniform heterodimerization based on some plausible mechanisms in biology. We show that our model cannot only reproduce scale-free connectivity and small-world pattern, but also exhibit hierarchical modularity and disassortativity. After comparing the features of our model with those of real protein-protein interaction networks, we believe that our model can provide relevant insights into the mechanism underlying the evolution of protein-protein interaction networks.     

关于Kuramoto-Sivashinsky方程的吸收集半径

给出了Ｋｕｒａｍｏｔｏ＿Ｓｉｖａｓｈｉｎｓｋｙ方程吸收集半径的优化估计·证明了，当粘性系数趋向某临界值时，吸收集半径将趋于零·这与已有结果比更符合物理直观·     

ON RADII OF ABSORBING SETS FOR KURAMOTOSIVASHINSKY EQUATION

１ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄｔｈｅＭａｉｎＴｈｅｏｒｅｍＩｔｉｓｋｎｏｗｎｔｈａｔｔｈｅｉｎｅｒｔｉａｌｍａｎｉｆｏｌｄｉｓａｐｏｗｅｒｆｕｌｔｏｌｆｏｒｒｅｄｕｃｉｎｇａｎｉｎｆｉｎｉｔｅ＿ｄｉｍｅｎｓｉｏｎａｌｄｙｎａｍｉｃａｌｓｙｓｔｅｍｔ...     

THE MATRIC ALGORITHM OF LYAPUNOV EXPONENT FOR THE EXPERIMENTAL DATA OBTAINED IN DYNAMIC ANALYSIS

ＩｎｔｒｏｄｕｃｔｉｏｎＣｈａｏｓｉｓａｎｉｒｒｅｇｕｌａｒｐｈｅｎｏｍｅｎｏｎｇｅｎｅｒａｔｅｄｂｙｎｏｎｌｉｎｅａｒｍｏｄｅｌｓ．Ｉｔｅｘｔｅｎｓｉｖｅｌｙｅｘｉｓｔｓｉｎｎａｔｕｒｅ．Ｗｈｅｎａｒｅａｌｉｒｒｅｇｕｌａｒｔｉｍｅｓｅｒｉｅｓｉｓｇｉｖｅｎ，ｐｅｏｐｌｅｗｉｌｌｓｐｏｎｔａｎｅｏｕｓｌｙａｓｋｔｈｅｑｕｅｓｔｉｏｎ：ｗｈｅｔｈｅｒｔｈｅｔｉｍｅｓｅｒｉｅｓｉｓｐｒｏｃｅｓｓａｓｒａｎｄｏｍｏｒａｓｄｅｔｅｒｍｉｎｉｓｔｉｃｃｈａｏｓ．Ｉｆｔｈｅｔｉｍｅｓｅｒｉｅｓｉｓｔｈｅｒ…     

混沌网络的聚类同步方法

由于通讯技术和生物工程等科学的发展，许多的聚类同步现象陆续被发 现和研究. 然而，由于网络的复杂性，有关聚类同步的理论结果极少见报道. 从上述问题出发，对于大小为N=mn的网络, 通过构造带权重的相互作用，得 到了n个聚类的聚类同步，其中每个聚类的振子数目都等于m. 最后， 以耦合Lorenz系统为例，验证了以上结果的正确性.