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1.
Isochronicity and normal forms of polynomial systems of ODEs
Maoan Han, Valery Romanovski, 2012, published scientific conference contribution

Abstract: We propose a generalization of the notion of isochronicity for real polynomial autonomous systems to the case of complex two dimensional systems of ODEs. We study the generalized problem in the case of a quadratic system and a system with homogeneous cubic nonlinearities. Main tools of the study are algorithms of computational algebra based on the Groebner basis theory.
Keywords: polynomial systems of ODE`s, isochronicity, linearizability, normal forms
Published: 10.07.2015; Views: 553; Downloads: 79
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2.
The study of isochronicity and critical period bifurcations on center manifolds of 3-dim polynomial systems using computer algebra
Matej Mencinger, Brigita Ferčec, 2013, published scientific conference contribution

Abstract: Using the solution of the center-focus problem from [4], we present the investigation of isochronicity and critical period bifurcations of two families of cubic 3-dim systems of ODEs. Both cubic systems have a center manifold filled with closed trajectories. The presented study is performed using computer algebra systems Mathematica and Singular.
Keywords: polynomial systems of ODEs, center manifolds, isochronicity, bifurcation of critical periods, CAS
Published: 10.07.2015; Views: 658; Downloads: 44
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