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In this paper we study the existence and non-existence of limit cycles for the class of polynomial differential systems of the form x ̇ = λ x + P n (x , y) , y ̇ = μ y + Q n (x , y) , where P n and Q n are homogeneous polynomials of degree n. [ABSTRACT FROM AUTHOR]

Abstract: We characterize the integrability and the non-existence of periodic orbits for the 2-dimensional Kolmogorov systems of the form where n and m are positive integers and and are homogeneous polynomials of degree and m, respectively. [Copyright &y& Elsevier]

Abstract: We consider the class of polynomial differential equations , , in where and are homogeneous polynomials of degree and , i.e. the class of polynomial differential systems with homogeneous nonlinearities with a star node at the origin. We prove that these systems are Darboux integrable. Moreover, for these systems we study the existence and non-existence of limit cycles surrounding the equilibrium point located at the origin. [Copyright &y& Elsevier]