Learn More
In this paper, we prove the existence of twelve small (local) limit cycles in a planar system with third-degree polynomial functions. The best result so far in literature for a cubic order planar system is eleven limit cycles. The system considered in this paper has a saddle point at the origin and two focus points which are symmetric about the origin. This(More)
OBJECTIVE Results of previous studies suggest that anti-beta2-glycoprotein I (anti-beta2GPI) antibodies in complex with beta2GPI activate platelets in a dysregulated manner, potentially contributing to the prothrombotic tendency associated with the antiphospholipid syndrome (APS). We undertook this study to investigate the possible contribution of the(More)
Angiopoietin-like protein 1 (ANGPTL1) is a potent regulator of angiogenesis. Growing evidence suggests that ANGPTL family proteins not only target endothelial cells but also affect tumor cell behavior. In a screen of 102 patients with lung cancer, we found that ANGPTL1 expression was inversely correlated with invasion, lymph node metastasis, and poor(More)
A general explicit formula is derived for controlling bifurcations using nonlinear state feedback. This method does not increase the dimension of the system, and can be used to either delay (or eliminate) existing bifurcations or change the stability of bifurcation solutions. The method is then employed for Hopf bifurcation control. The Lorenz equation and(More)
In this paper, the existence of 12 small limit cycles is proved for cubic order Z2-equivariant vector fields, which bifurcate from fine focus points. This is a new result in the study of the second part of the 16th Hilbert problem. The system under consideration has a saddle point, or a node, or a focus point (including center) at the origin, and two weak(More)
This paper considers the problems of stability, stabilization and H∞ control via memoryless state feedback for uncertain discrete-time Markovian jump linear systems with mode-dependent time delays. Based on linear matrix inequalities, delay-dependent solutions are obtained by using a descriptor model transformation of the system and by applying a new(More)
The focus of the paper is mainly on the existence of limit cycles of a planar system with thirddegree polynomial functions. A previously developed perturbation technique for computing normal forms of differential equations is employed to calculate the focus values of the system near equilibrium points. Detailed studies have been provided for a number of(More)
In this paper, the concept of globally exponentially attractive set is proposed and used to consider the ultimate bounds of the family of Lorenz systems with varying parameters. Explicit estimations of the ultimate bounds are derived. The results presented in this paper contain all the existing results as special cases. In particular, the critical cases, b(More)
This paper considers the globally exponential synchronization (GES) of the family of Rössler chaotic systems. One pair of the six transmitter-receiver systems is specifically studied, and algebraic criterion for the GES is obtained via proper nonlinear feedback controls. Based on the study of the systems’ structures, appropriate Lyapunov functions are(More)
This paper presents some new results which we obtained recently for the study of limit cycles of nonlinear dynamical systems. Particular attention is given to small limit cycles of generalized Liénard systems in the vicinity of the origin. New results for a number of cases of the Liénard systems are presented with the Hilbert number, b H ði; jÞ 1⁄4 b H ðj;(More)