共查询到18条相似文献,搜索用时 109 毫秒
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研究一类平面微分系统的极限环,利用Hopf分支理论得到了该系统极限环存在性与稳定性的若干充分条件,利用Л.A.Чepkac和Л.ИЖилевьыч的唯一性定理得到了极限环唯一性的若干充分条件. 相似文献
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研究一类平面2n 1次多项式微分系统的极限环问题,利用Hopf分枝理论得到了该系统极限环存在性与稳定性的若干充分条件,利用Cherkas和Zheilevych的唯一性定理得到了极限环唯一性的若干充分条件. 相似文献
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包围多个奇点的极限环的唯一性与唯二性 总被引:8,自引:0,他引:8
本文研究具多个奇点的 Liènard 方程,得到极限环唯一性和唯二性的若干充分条件,即使在奇点唯一的情况下,这些条件也是与以往唯一性条件具有不同的形式. 相似文献
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讨论了一类三次系统x=-y(1-βx2)-(a1x a2x2 a3x3),y=b1x b2x2 b3x3的极限环问题.对包含一个奇点或多个奇点的极限环的唯一性和唯二性给出了若干充分条件. 相似文献
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研究捕食者与食饵均具有线性密度制约的Ivlev型捕食动力系统.应用常微分方程定性方法,得到了正平衡点的全局稳定性和非小振幅极限环的存在唯一性的充分条件.特别地,在一定条件下,证明了极限环的存在唯一性与正平衡点的局部不稳定性是等价的,正平衡点的局部稳定性隐含它的全局稳定性,因此,系统的全局动力学性质完全由正平衡点的局部性质所决定. 相似文献
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Relationships between limit cycles and algebraic invariant curves for quadratic systems 总被引:1,自引:0,他引:1
Jaume Llibre 《Journal of Differential Equations》2006,229(2):529-537
Algebraic limit cycles for quadratic systems started to be studied in 1958. Up to now we know 7 families of quadratic systems having algebraic limit cycles of degree 2, 4, 5 and 6. Here we present some new results on the limit cycles and algebraic limit cycles of quadratic systems. These results provide sometimes necessary conditions and other times sufficient conditions on the cofactor of the invariant algebraic curve for the existence or nonexistence of limit cycles or algebraic limit cycles. In particular, it follows from them that for all known examples of algebraic limit cycles for quadratic systems those cycles are unique limit cycles of the system. 相似文献
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Jiafu Wang Xiaoyan Chen Lihong Huang 《Journal of Mathematical Analysis and Applications》2019,469(1):405-427
The objective of this paper is to study the number and stability of limit cycles for planar piecewise linear (PWL) systems of node–saddle type with two linear regions. Firstly, we give a thorough analysis of limit cycles for Liénard PWL systems of this type, proving one is the maximum number of limit cycles and obtaining necessary and sufficient conditions for the existence and stability of a unique limit cycle. These conditions can be easily verified directly according to the parameters in the systems, and play an important role in giving birth to two limit cycles for general PWL systems. In this step, the tool of a Bendixon-like theorem is successfully employed to derive the existence of a limit cycle. Secondly, making use of the results gained in the first step, we obtain parameter regions where the general PWL systems have at least one, at least two and no limit cycles respectively. In addition for the general PWL systems, some sufficient conditions are presented for the existence and stability of a unique one and exactly two limit cycles respectively. Finally, some numerical examples are given to illustrate the results and especially to show the existence and stability of two nested limit cycles. 相似文献
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This paper concerns with limit cycles through Hopf and homoclinic bifurcations for near-Hamiltonian systems. By using the coefficients appeared in Melnikov functions at the centers and homoclinic loops, some sufficient conditions are obtained to find limit cycles. 相似文献
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Deming Zhu 《应用数学学报(英文版)》1991,7(2):108-113
The cycle control function is defined and used to estimate the number of limit cycles for some planar autonomous systems. Some sufficient conditions for the existence of no or at most one limit cycle are given. 相似文献
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We investigate the existence and number of limit cycles in a class of general planar piecewise linear systems constituted by two linear subsystems with node–node dynamics. Using the Liénard-like canonical form with seven parameters, some sufficient and necessary conditions for the existence of limit cycles are given by studying the fixed points of proper Poincaré maps. In particular, we prove the existence of at least two nested limit cycles and describe some parameter regions where two limit cycles exist. The main results are applied to the PWL Morris–Lecar neural model to determine the existence and stability of the limit cycles. 相似文献
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In this paper, we characterize local behavior of an isolated nilpotent critical point for a class of septic polynomial differential systems, including center conditions and bifurcation of limit cycles. With the help of computer algebra system-MATHEMATICA 12.0, the first 15 quasi-Lyapunov constants are deduced. As a result, necessary and sufficient conditions of such system having a center are obtained. We prove that there exist 16 small amplitude limit cycles created from the third-order nilpotent critical point. And then we give a lower bound of cyclicity of third-order nilpotent critical point for septic Lyapunov systems. 相似文献
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给出系统(E1),(E2)和(E3)等非线性微分系统存在闭轨的一些新的判定条件,推广了非线性微分系统极限环的存在性和唯一性许多这方面研究的结果,并大大改进了它们的某些条件.在这个基础上,还给出了系统(E1)和(E2)恰有一个极限环的一组充分条件. 相似文献
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