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 lim...

Article history: Received 1 May 2011 Accepted 15 February 2012 Available online 16 March 2012 0960-0779/$ see front matter 2012 Elsevier Ltd doi:10.1016/j.chaos.2012.02.010 ⇑ Corresponding author at: Department of Applied E-mail address: [email protected] (P. Y In this paper, we consider bifurcation of limit cycles in planar quadratic Hamiltonian systems with various degree polynomial per...

In this paper we consider the bifurcation of limit cycles of the system ˙ x = y(x 2 − a 2)(y 2 − b 2) + εP(x, y), ˙ y = −x(x 2 − a 2)(y 2 − b 2) + εQ (x, y) for ε sufficiently small, where a, b ∈ R − {0}, and P, Q are polynomials of degree n, we obtain that up to first order in ε the upper bounds for the number of limit cycles that bifurcate from the period annulus of the quintic center given b...

Consider a polynomial Liénard system depending on three parameters a, b, c and with the following properties: (i) The origin is the unique equilibrium for all parameters. (ii). If a crosses zero, then the origin changes its stability, and a limit cycle bifurcates from the equilibrium. We investigate analytically this bifurcation in dependence on the parameters b and c and establish the existenc...

Liénard equations, ẍ+ ǫf(x)ẋ+ x = 0, with f(x) an even continuous function are considered. In the weakly nonlinear regime (ǫ → 0), the number and a O(ǫ0) approximation of the amplitude of limit cycles present in this type of systems, can be obtained by applying a methodology recently proposed by the authors [López-Ruiz R, López JL. Bifurcation curves of limit cycles in some Liénard systems. Int...

mong the various bifurcation phenomena that may be observed in dynamical systems, gluing bifurcation is an important class of homoclinic bifurcation. The Z2 (or the so called reflection) symmetry plays a crucial role in occurrence of such bifurcation. At the bifurcation point two homoclinic orbits, which are mirror image of each other, appear as glued together at the saddle and thus forming in ...

Mathematically, bifurcation theory attempts to investigate the changes in the qualitative or topological structure of a studied equation models. Given paper focuses on an analytical investigation of the nonlinear behavior of an indirect filedoriented control of induction motor. In this context, steady-state responses of the motor model are discussed and an analytical study of the generic codime...