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Keywords: Resonant center problem First integral Lotka–Volterra systems a b s t r a c t In this paper we obtain conditions on the coefficients of a cubic Lotka–Volterra system of the form _ x ¼ xð2 À a 20 x 2 À a 11 xy À a 02 y 2 Þ; _ y ¼ yðÀ3 þ b 20 x 2 þ b 11 xy þ b 02 y 2 Þ; ð1Þ which fulfillment yields the existence in a neighborhood of the origin of a(More)
The main objective of this paper is to find necessary and sufficient conditions for a 1 : −4 resonant system of the form ˙ x = x − a10x 2 − a01xy − a12y 2 , ˙ y = −4y + b2,−1x 2 + b10xy + b01y 2 to have a center at the origin. Since applying a linear change of variables any system of this form can be transformed either to system with a10 = 1 or a10 = 0,(More)
This study evaluated, in vitro, the antimicrobial activity of the hexane extract (JCHE), methanol extract (JCME), and chloroform fraction (JCCF) of bark from Jacaranda cuspidifolia Mart. (Family Bignoniaceae), a Brazilian medicinal plant, traditionally used as anti-syphilis and anti-gonorrhea treatment. The antimicrobial activity was evaluated using the(More)
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