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141.
142.
Limit cycles for two classes of planar polynomial differential systems with uniform isochronous centers
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In this article, we study the maximum number of limit cycles for two classes of planar polynomial differential systems with uniform isochronous centers. Using the first-order averaging method, we analyze how many limit cycles can bifurcate from the period solutions surrounding the centers of the considered systems when they are perturbed inside the class of homogeneous polynomial differential systems of the same degree. We show that the maximum number of limit cycles, $m$ and $m+1$, that can bifurcate from the period solutions surrounding the centers for the two classes of differential systems of degree $2m$ and degree $2m+1$, respectively. Both of the bounds can be reached for all $m$. 相似文献
143.
Jaume Giné 《Journal of Applied Analysis & Computation》2011,1(4):487-496
In this short survey we study the narrow relation between the center problem and the Lie symmetries. It is well known that an analytic vector eld X having a non-degenerate center has a non-trivial analytic Lie symmetry in a neighborhood of it, i.e. there exists an analytic vector eld Y such that [X;Y] = \(\mu\)X. The same happens for a nilpotent center with an analytic rst integral as can be seen from the last results about nilpotent centers. From the last results for nilpotent and degenerate centers it also can be proved that any nilpotent or degenerate center has a trivial smooth (of class \(C^{\infty} \) ) ) Lie symmetry. Remains open if always exists also a non-trivial Lie symmetry for any nilpotent and degenerate center. 相似文献
144.
145.
In this paper, we derive a semi-discrete system for a nonlinear model of blood cell production. The local stability of its fixed points is investigated by employing a key lemma from [23, 24]. It is shown that the system can undergo Neimark-Sacker bifurcation. By using the Center Manifold Theorem, bifurcation theory and normal form method, the conditions for the occurrence of Neimark-Sacker bifurcation and the stability of invariant closed curves bifurcated are also derived. The numerical simulations verify our theoretical analysis and exhibit more complex dynamics of this system. 相似文献
146.
Jaume Gine Jaume Llibre Claudia Valls 《Journal of Applied Analysis & Computation》2017,7(4):1534-1548
For the polynomial differential system $\dot{x}=-y$, $\dot{y}=x +Q_n(x,y)$, where $Q_n(x,y)$ is a homogeneous polynomial of degree $n$ there are the following two conjectures done in 1999. (1) Is it true that the previous system for $n \ge 2$ has a center at the origin if and only if its vector field is symmetric about one of the coordinate axes? (2) Is it true that the origin is an isochronous center of the previous system with the exception of the linear center only if the system has even degree? We give a step forward in the direction of proving both conjectures for all $n$ even. More precisely, we prove both conjectures in the case $n = 4$ and for $n\ge 6$ even under the assumption that if the system has a center or an isochronous center at the origin, then it is symmetric with respect to one of the coordinate axes, or it has a local analytic first integral which is continuous in the parameters of the system in a neighborhood of zero in the parameters space. The case of $n$ odd was studied in [8]. 相似文献
147.
Xingwu Chen Valery G. Romanovski 《Journal of Mathematical Analysis and Applications》2010,362(2):129-189
In this paper we present the necessary and sufficient conditions for linearizability of the planar time-reversible cubic complex system , . From these conditions, the necessary and sufficient conditions for the origin to be an isochronous center of the time-reversible cubic real system , can be obtained. Thus, the isochronous center problem of time-reversible cubic systems is solved completely. 相似文献
148.
Géraldine Bous Philippe Fortemps François Glineur Marc Pirlot 《European Journal of Operational Research》2010
In multiple criteria decision aiding, it is common to use methods that are capable of automatically extracting a decision or evaluation model from partial information provided by the decision maker about a preference structure. In general, there is more than one possible model, leading to an indetermination which is dealt with sometimes arbitrarily in existing methods. This paper aims at filling this theoretical gap: we present a novel method, based on the computation of the analytic center of a polyhedron, for the selection of additive value functions that are compatible with holistic assessments of preferences. We demonstrate the most important characteristics of this technique with an experimental and comparative study of several existing methods belonging to the UTA family. 相似文献
149.
We propose both robust and data-driven approaches to a fluid model of call centers that incorporates random arrival rates with abandonment to determine staff levels and dynamic routing policies. We test the resulting models with real data obtained from the call center of a US bank. Computational results show that the robust fluid model is significantly more tractable as compared to the data-driven one and produces overall better solutions to call centers in most experiments. 相似文献
150.
<正>Motivated by an animal territoriality model,we consider a centroidal Voronoi tessellation algorithm from a dynamical systems perspective.In doing so,we discuss the stability of an aligned equilibrium configuration for a rectangular domain that exhibits interesting symmetry properties.We also demonstrate the procedure for performing a center manifold reduction on the system to extract a set of coordinates which capture the long term dynamics when the system is close to a bifurcation.Bifurcations of the system restricted to the center manifold are then classified and compared to numerical results.Although we analyze a specific set-up,these methods can in principle be applied to any bifurcation point of any equilibrium for any domain. 相似文献