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pll方程
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  pll equations
     Chaos and Subharmonic Bifurcations for a Family of PLL Equations
     一类PLL方程的混沌与次谐波分支
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     In section 6, the main results are given. In the second part, a family of PLL equations are investigated by using Melnikov method. the existence of chaos in the sense of Smale horseshoes is showen and the partitions of the regions of chaos and subharmonic bifurcations are obtained.
     第六节给出了主要结果第二部分利用Melnikov方法研究了一类PLL方程,证明了该系统Smale马蹄型混沌及次谐波的存在性,并并分别给出了其混沌区域及次谐波分支区域本部分由四节组成,第一节介绍了Melnikov方法及所要研究的系统;
短句来源
     In this paper,by using the method,a family of PLL equations are studied to show the existence of subharmonic solutions and chaos in the sense of Smale horseshoes. The regions of chaos and subharmonic bifurcations are given.
     文中利用该方法研究了一类PLL方程,证明了该系统次谐波及Smale马蹄意义下的混沌的存在性,并给出了混沌区域及次谐波分支区域.
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  相似匹配句对
     PLL.
     PLL.
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     Synthetic Aperture Radar Equations
     合成孔径雷达方程
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     Chaos and Subharmonic Bifurcations for a Family of PLL Equations
     一类PLL方程的混沌与次谐波分支
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     THE EQUATION OF MAGNETIC LINE OF FORCE
     磁力线方程
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  pll equation
Verified inclusion for eigenvalues of the first order PLL equation with general phase detector characteristics
      


In this paper, let ε=u +vp be fundamental solution of the Pell equation

本文我们进一步得到方程q~m=p~n+2,p,q是素数,m>1,n>1(*)无解的一些结果:(1)设q=p+4+6a或p=q+2+6a,则除开3~3=5~2+2以外方程(*)无解.设ε=u+v(p~(1/P)是pll方程x~2-py~2=1的基本解,我们有(2)设q=p+6a或p=q+6a,则当u≠1/2(q~m+p~n)或v≠q~(m/2)p~(n-1/2)时方程无解.(3)设q=p+2+6a,p>3,a≠0(mod4)或p=q+4+6a,q>3,a≠3(mod4),则当u≠1/2(q~m+p~n)或v≠q(m/2)p(n-1/2)时方程(*)无解.

Melnikov method is an effectively mathematical method which is usually used to prove the existence of chaos in the sense of Smale horseshoes.By measuring the distance between the stable manifold and the unstable manifold of the hyperbolic fixed point in the Poincare map,it is shown whether the system has transversally homoclinicpoints and chaos in the sense of Smale horseshoes.Under the certain conditions,it can also be used to study the subharmonic bifurcations of some nonlinear systems.In this paper,by using...

Melnikov method is an effectively mathematical method which is usually used to prove the existence of chaos in the sense of Smale horseshoes.By measuring the distance between the stable manifold and the unstable manifold of the hyperbolic fixed point in the Poincare map,it is shown whether the system has transversally homoclinicpoints and chaos in the sense of Smale horseshoes.Under the certain conditions,it can also be used to study the subharmonic bifurcations of some nonlinear systems.In this paper,by using the method,a family of PLL equations are studied to show the existence of subharmonic solutions and chaos in the sense of Smale horseshoes.The regions of chaos and subharmonic bifurcations are given.

Melnikov方法是用来判定一个系统是否存在Smale马蹄意义下的混沌的一种有效的数学方法,它通过测量Poincare映射的双曲不动点的稳定流形与不稳定流形之间的距离来判定系统横截同宿点的存在性及Smale马蹄意义下的混沌的存在性.在一定条件下,Melnikov方法还可以用来研究非线性系统的次谐波分支.文中利用该方法研究了一类PLL方程,证明了该系统次谐波及Smale马蹄意义下的混沌的存在性,并给出了混沌区域及次谐波分支区域.

 
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