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We apply the averaging theory of first, second and third order to the class of generalized polynomial Liénard differential equations. Our main result shows that for any n, m ≥ 1 there are differential equations of the form¨x + f (x) ˙ x + g(x) = 0, with f and g polynomials of degree n and m respectively, having at least [(n + m − 1)/2] limit cycles, where(More)
Brassinosteroids are a new class of plant hormones with a polyoxygenated steroid structure showing pronounced plant growth regulatory activity. This review covers their natural occurrence, biological and chromatographic methods for their detection, biosynthesis and metabolism, biological activity, structure-activity relationships and prospective(More)
We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1 : 1 internal resonance in the cases of weak and strong coupling. Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours. A two-time scales method is used to(More)
In the present study, a Brazilian population, located in the Rondônia state, was genetically characterized for a set of Y chromosome specific STRs included in the Applied Biosystems kit (AmpFℓSTR®Yfiler™), which allows the simultaneous amplification of 16 markers: DYS19, DYS389I, DYS389II, DYS390, DYS391, DYS392, DYS393, DYS385a/b, DYS438, DYS439, DYS437,(More)
(Communicated by Aim Sciences) Dedicated to Carlos Gutierrez and Marco Antonio Teixeira on the occasion of their 60th birthdays. Abstract. We study geometric properties of the integral curves of an implicit differential equation in a neighbourhood of a codimension ≤ 1 singularity. We also deal with the way these singularities bifurcate in generic families(More)
In this paper we study piecewise linear differential systems formed by two regions separated by a straight line so that each system has a real saddle point in its region of definition. If both saddles are conveniently situated, they produce a transition flow from a segment of the splitting line to another segment of the same line, and this produces a(More)