共查询到17条相似文献,搜索用时 78 毫秒
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关于二次微分系统Ⅰ类方程的极限环之二 总被引:2,自引:0,他引:2
本文研究了二次微分系统Ⅰ类方程dx/dt=-y+δx+lx2+mxy+ny2,dy/dt=x的极限环问题,得到了当lι≠0时大范围内存在极限环的条件. 相似文献
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关于二次微分系统I类方程的极限 总被引:7,自引:1,他引:6
本文研究二次微分系统I类方程dx/dt=-y+δx+lx2+mxy+ny2,dy/dt=x的极限问题,得到了当l=0时大范围内存在极限环的条件,并探讨了与之有关的分界线环和分歧曲线的存在问题. 相似文献
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本文研究一般二次系统在两个焦点 O(0,0)和(?)(0,1/n)附近极限环的不同时存在性,得到了几个新的判别准则。方法是用了一个简单的变换。 相似文献
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叶惟寅 《高校应用数学学报(A辑)》1999,14(3):254-260
在假设文中命题A成立的条件下证明了一般二次微分系统的极限环所有可能的分布为(3,1),(1,3),(3,0),(0,3),(2,1),(1,2),(2,0),(1,1),(0,2),(1,0),(0,1)和(0,0)。 相似文献
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证明了一般的Ⅲ类二次系统当参数a很小时极限环的大范围惟一性,对于一般的参数值a,在适当的条件下也证明了极限环的大范围惟一性.文中也给出了极限环随参数d变化时产生和消失的过程. 相似文献
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In this paper we give the necessary and sufficient conditions for all finite critical points of quadratic differential systems
to be weak foci, and solve an open problem proposed by Yanquian Ye.
Received January 11, 1999, Revised October 10, 2000, Accepted March 5, 2001 相似文献
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本文对系统dxdt=-y(1-ax2n)(1-bx2n) δx-lx4n 1dydt=x2n-1(1-cx2n)(1-bx2n)进行定性分析,得出其极限环的存在性,不存在性及唯一性的一系列充分条件. 相似文献
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具有二个焦点的二次系统极限环的分布与个数 总被引:6,自引:0,他引:6
本文证明了具有二个焦点的二次系统必在其中一个焦点外围至多有一个极限环这一猜想.从而得到具有二个焦点的二次系统之极限环必是(O,i)或(1,i)分布(i= 0, 1, 2,). 相似文献
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This paper is concerned with limit cycles which bifurcate from a period annulus of a quadratic reversible Lotka-Volterra system with sextic orbits. The authors apply the property of an extended complete Chebyshev system and prove that the cyclicity of the period annulus under quadratic perturbations is equal to two. 相似文献
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In this paper, the bifurcation of limit cycles for planar piecewise smooth systems is studied which is separated by a straight line. We give a new form of Abelian integrals for piecewise smooth systems which is simpler than before. In application, for piecewise quadratic system the existence of 10 limit cycles and 12 small-amplitude limit cycles is proved respectively. 相似文献
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Brigita Ferče Ilona Nagy Valery G. Romanovski Gábor Szederkényi János Tóth 《Journal of Nonlinear Modeling and Analysis》2019,1(3):283-300
Kinetic differential equations, being nonlinear, are capable of producing many kinds of exotic phenomena. However, the existence of multistationarity, oscillation or chaos is usually proved by numerical methods. Here we investigate a relatively simple reaction among two species consisting of five reaction steps, one of the third order. Using symbolic methods we find the necessary and sufficient conditions on the parameters of the kinetic differential equation of the reaction under which a limit cycle bifurcates from the stationary point in the positive quadrant in a supercritical Hopf bifurcation. We also performed the search for partial integrals of the system and have found one such integral. Application of the methods needs computer help (Wolfram language and the Singular computer algebra system) because the symbolic calculations to carry out are too complicated to do by hand. 相似文献