Limit Cycles of a Quadratic System with Two Parallel Straight Line - Isoclines ⋆
نویسنده
چکیده
In this paper, a quadratic system with two parallel straight line-isoclines is considered. This system corresponds to the system of class II in the classification of Ye Yanqian [13]. Using the field rotation parameters of the constructed canonical system and geometric properties of the spirals filling the interior and exterior domains of its limit cycles, we prove that the maximum number of limit cycles in a quadratic system with two parallel straight line-isoclines and two finite singular points is equal to two. Besides, we obtain the same result in a different way: applying the Wintner–Perko termination principle for multiple limit cycles and using the methods of global bifurcation theory developed in [7].
منابع مشابه
Bifurcation of limit cycles from a quadratic reversible center with the unbounded elliptic separatrix
The paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of a quadratic reversible and non-Hamiltonian system, whose period annulus is bounded by an elliptic separatrix related to a singularity at infinity in the poincar'{e} disk. Attention goes to the number of limit cycles produced by the period annulus under perturbations. By using the appropriate Picard...
متن کاملOn the Number of Limit Cycles in Discontinuous Piecewise Linear Differential Systems with Two Pieces Separated by a Straight Line
In this paper we study the maximum number N of limit cycles that can exhibit a planar piecewise linear differential system formed by two pieces separated by a straight line. More precisely, we prove that this maximum number satisfies 2 ≤ N ≤ 4 if one of the two linear differential systems has its equilibrium point on the straight line of discontinuity.
متن کاملAnalysis of 3D Passive Walking Including Turning Motions for the Finite-width Rimless Wheel
The focus of studies in the field of passive walking has often been on straight walking, while less attention has been paid to the field of turning motions. In this paper, the passive motions of a finite width rimless wheel as the simplest 3D model of passive biped walkers was investigated with a focus on turning motions. For this purpose, the hybrid model of the system consisting of continuous...
متن کاملOn the Number of Limit Cycles of Planar Quadratic Vector Fields with a Perturbed Center
We investigate the number of limit cycles of a planar quadratic vector field with a perturbed center-like singular point. An upper bound is obtained on the number of δ-good limit cycles of such a vector field (Theorem 1). Here δ is a parameter characterizing the limit cycles: it shows how far those cycles are from the singular points of the vector field and from the infinite points. The bound a...
متن کاملSimulation of Metro Train Fire in an Underground Station of Tehran Metro Line 7
In this research a fire scenario was simulated in one of the stations of the line 7 of Tehran's subway system. The Line 7 is under construction and the ventilation system is under design. Fire was set for a stopping metro train at the platform of the station. A 160 meter length eight-car metro train with the forth wagon on the fire was studied. The heat release rate is based on a quadratic f...
متن کامل