The Cyclicity of Period Annuli of Some Classes of Reversible Quadratic Systems
نویسندگان
چکیده
The cyclicity of period annuli of some classes of reversible and non-Hamiltonian quadratic systems under quadratic perturbations are studied. The argument principle method and the centroid curve method are combined to prove that the related Abelian integral has at most two zeros.
منابع مشابه
The Cyclicity of Period Annuli of a Quadratic Reversible Lotka-Volterra System with Two Centers
This paper is concerned with the bifurcations of limit cycles in a quadratic reversible Lotka-Volterra system with two centers under quadratic perturbations. By studying the number of zeros of Abelian integral based on the geometric properties of some planar curves, we obtain the cyclicity of each periodic annulus of the system under quadratic perturbations is two, and the cyclicity of two peri...
متن کاملBifurcation 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 کاملLimit cycles for a quadratic perturbation of a quadratic polynomial system
The weak Hilbert 16th problem was solved completely in the quadratic case; that is, the least upper bound of the number of zeros of the Abelian integrals associated with quadratic perturbations of quadratic Hamiltonian systems is known. See [3, 4, 5, 8, 10] and the references therein. The next natural step is to consider the same problem for quadratic integrable but non-Hamiltonian systems. Mos...
متن کاملSome classes of strongly clean rings
A ring $R$ is a strongly clean ring if every element in $R$ is the sum of an idempotent and a unit that commutate. We construct some classes of strongly clean rings which have stable range one. It is shown that such cleanness of $2 imes 2$ matrices over commutative local rings is completely determined in terms of solvability of quadratic equations.
متن کاملThe Sine-Cosine Wavelet and Its Application in the Optimal Control of Nonlinear Systems with Constraint
In this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. The sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. Then, the Newton-Raphson method is used for solving these sets of algebraic equations. To present ability ...
متن کامل