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广义Liénard系统的同宿轨族与闭轨族 总被引:1,自引:0,他引:1
1引言 众所周知,关于广义Liénard系统 (·x)=h(y)-F(x), (y)=-g(x) (1) 的同宿轨与闭轨族的研究非常少.受[1,2]的启发,本文考虑(1)不具有条件F(-x)=F(x),g(-x)=-g(x)时这方面解的一些定性性质,得到了同宿轨族、闭轨族、双曲扇形和椭圆扇形的存在性与不存在性的充分或充要条件. 相似文献
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Lienard系统的同宿轨族与闭轨族 总被引:4,自引:0,他引:4
本文讨论Lienard系统解的一些定性性质,得到了存在同宿轨族、闭轨族、双曲扇形和椭圆扇形、正负半轨有界及其与等倾线相交的充要条件或充分条件. 相似文献
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Liénard系统的同宿轨族与闭轨族 总被引:5,自引:1,他引:4
本文讨论Lienard系统解的一些定性性质,得到了存在同宿轨族、闭轨族、双曲扇形和椭圆扇形、正负半轨有界及其与等倾线相交的充要条件或充分条件. 相似文献
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利用向量场的旋度 ,我们可判定平面、空间微分系统闭轨的不存在性 ,得到类似 Bendixson,Dulac判断法的一种新判定法 .同时还得到平面微分系统闭轨存在时的相对位置 相似文献
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周毓荣 《数学年刊A辑(中文版)》1989,(4)
本文利用孤立块和动力系统中典型区域的工具,给出了存在连结微分方程的两个奇点的轨线的几个充要条件,揭示了连结奇点的轨线与闭轨线、奇异闭轨线及分界线的关系。 相似文献
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几类非线性微分方程闭轨线的不存在性 总被引:1,自引:0,他引:1
本文研究几类非线性微分方程不存在闭轨线的条件,所得结果可用于判别方程■ f_1(x)■ f_2(x)■ g(x)=0和■ f(x,■)■ g(x)=0闭轨线的不存在性. 相似文献
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This paper is devoted to existence of trajectories to differential equations and inclusions remaining in a given closed (or compact) set. Topological properties of the boundary of this set enables us to conclude the existence of such trajectories in many cases. 相似文献
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V. P. Golubyatnikov I. V. Golubyatnikov V. A. Likhoshvai 《Numerical Analysis and Applications》2010,3(4):329-335
Sufficient conditions for the existence and stability of closed trajectories in five-dimensional nonlinear dynamical systems that model gene networks with negative feedback are obtained. 相似文献
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V. P. Golubyatnikov I. V. Golubyatnikov 《Journal of Applied and Industrial Mathematics》2011,5(3):343-347
Some sufficient conditions are obtained for the existence of closed trajectories of the odd-dimensional nonlinear dynamical systems that model gene networks with negative feedbacks. 相似文献
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Shuliang Shui Xuyang Zhang Jingjing Li 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(5):1277-1288
We use the theory of differential inclusions, Filippov transformations and some appropriate Poincaré maps to discuss the special case of two-dimensional discontinuous piecewise linear differential systems with two zones. This analysis applies to uniqueness and non-uniqueness for the initial value problem, stability of stationary points, sliding motion solutions, number of closed trajectories, existence of heteroclinic trajectories connecting two saddle points forming a heteroclinic cycle and existence of the homoclinic trajectory 相似文献
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V. V. Kozlov 《Proceedings of the Steklov Institute of Mathematics》2007,256(1):188-205
Properties of the solutions to differential equations on the torus with a complete set of multivalued first integrals are considered, including the existence of an invariant measure, the averaging principle, and the infiniteness of the number of zeros for integrals of zero-mean functions along trajectories. The behavior of systems with closed trajectories of large period is studied. It is shown that a generic system acquires a limit mixing property as the periods tend to infinity. 相似文献
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This work deals with a two-dimensional automatic control system containing a single nonlinear hysteretic element in the general form. The conditions sufficient for the existence of at least two limit cycles in the system are presented. To prove the existence of cycles, three closed contours embedded into each other are constructed on the phase manifold by “sewing” together pieces of the level lines of various Lyapunov functions. System trajectories cross the inner contour “from outside inwards” and the middle contour “from inside outwards.” The outer contour is crossed by system trajectories “from outside inwards.” The existence of these contours proves the presence of at least two limit cycles in the system. This paper is a continuation of our earlier published work “Conditions for the Global Stability of a Single System with Hysteresis Nonlinearity,” in which the conditions of global stability in this system are formulated. 相似文献
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In the paper we deal with differential inclusions with one-sided Lipschitz (OSL) continuous right-hand sides, and prove the existence of a continuous selection of the solution map which assigns to any point the set of solutions to the multivalued Cauchy problem. As an application we study the problem of the existence of viable trajectories in a prescribed closed subset of a Banach space via the generalized Wa?ewski retract method. 相似文献
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Aleksander Ćwiszewski 《Central European Journal of Mathematics》2011,9(2):244-268
A translation along trajectories approach together with averaging procedure and topological degree are used to derive effective
criteria for existence of periodic solutions for nonautonomous evolution equations with periodic perturbations. It is shown
that a topologically nontrivial zero of the averaged right hand side is a source of periodic solutions for the equations with
increased frequencies. Our setting involves equations on closed convex cones, therefore it enables us to study positive solutions
of nonlinear parabolic partial differential equations. 相似文献
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Paolo Nistri Marc Quincampoix 《Journal of Mathematical Analysis and Applications》2002,270(2):878-487
In this note, we investigate the existence of controls which allow to reach a given closed set K through trajectories of a nonlinear control system. In the case where the set is sufficiently regular we give a condition allowing to find a feedback control law which ensures the existence of trajectories to reach the set. We also consider the case where all the trajectories reach K. When K is not necessarily attainable but only viable, we build a set-valued feedback for which the set is invariant. Our approach concerns continuous dynamics, possibly not C1, so our methods do not come from geometric control theory. Furthermore, we do not require any regularity of the set K in order to obtain our results, except when we want to establish the existence of a feedback control law to achieve our goals. 相似文献
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Georges Haddad 《Israel Journal of Mathematics》1981,39(1-2):83-100
The paper gives a necessary and sufficient condition for the existence of monotone trajectories to differential inclusionsdx/dt ∈S[x(t)] defined on a locally compact subsetX ofR
p, the monotonicity being related to a given preorder onX. This result is then extended to functional differential inclusions with memory which are the multivalued case to retarded
functional differential equations. We give a similar necessary and sufficient condition for the existence of trajectories
which reach a given closed set at timet=0 and stay in it with the monotonicity property fort≧0. 相似文献