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Integrate and Fire Neural Networks, Piecewise Contractive Maps and Limit Cycles
Neural Networks Maps Limit Cycles
2010/11/11
We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are...
On the number of limit cycles in quadratic perturbations of quadratic codimension four centers
limit cycles quadratic codimension four centers
2010/11/15
This paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of quadratic codimension-four centers $Q_4$. Gavrilov and Iliev set an upper bound of {\it eight} for th...
We define a quantitative notion of shear for limit cycles of flows. We prove that strange attractors and SRB measures emerge when systems exhibiting limit cycles with sufficient shear are subjected to...
On Determinations of Limit Cycles.
Existence of Limit Cycles in a Predator-Prey System With a Functional Response of the Form Arctan(ax)
Predator prey system limit cycle unctional response
2008/11/25
We consider a predator prey system with the functional response of the form
µ(x) = arctan(ax); a > 0. The main concern in this paper is the existence of
limit cycles for such system. A necessa...
Bifurcation of limit cycles from quintic Hamiltonian with a double figure eight loop
动力系统 Conley理论 持续性 周期解 Abel积分
2008/4/25
Hilbert 16 问题的重要意义已是众所周知,但迄今尚未解决。为此，Arnold于1977年提出了弱Hilbert 16 问题，但也未解决。本项目首先研究与该问题有关的课题，讨论了三次和n次扰动的单参数Hamilton系统，得到了Abel积分的零点个数的上界估计。对具不变直线的二次系统极限环的唯一性定理，我们给出了完整的证明。对以柱面为首次积分的空间三次系统，我们得到在每个柱面上至多有三个周期...
Number and Location of Limit Cycles in a Class of Perturbed Polynomial Systems
polynomial system limit cycles stability bifurcation
2007/12/11
In this paper, we investigate the number, location andstability of limit cycles in a class of perturbed polynomialsystems with $(2n+1)$ or $(2n+2)$-degree by constructing detectionfunction and using q...
BIFURCATION OF LIMIT CYCLES FOR THE QUADRATIC DIFFERENTIAL SYSTEM (Ⅲ)l = n = 0
Quadratic system limit cycle
2007/12/10
In this paper we will prove that limit cycles for the quadratic differential system (Ⅲ)l=n=o in Chinese classification are concentratedly distributed, and that the maximum number of limit cycles aroun...
ON THE BOUNDEDNESS OF SOLUTIONS,EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF CUBIC DIFFERENTIAL SYSTEM
Boundedness of solutions limit cycle exi
2007/8/7
In this paper, we discuss the boundedness of the solutions, the existence and the uniqueness of the limit cycle of the following cubic differential system: x'=y, y'=-x+δy+a_2xy+a_4x+a_5x~2y. (*) We ob...
期刊信息
篇名
The Uniqueness of Limit Cycles for a Quadratic System with an Invariant Straight Line
语种
英文
撰写或编译
撰写
作者
周毓荣,王成文
第一作者单位
山东科技大学
刊物名称
International Journal of Pure and Applied Mathematics (SCI)
页...