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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)


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Mota, Marcos C. [1] ; Oliveira, Regilene D. S. [1]
Total Authors: 2
[1] Univ Sao Paulo, Dept Matemat, Inst Ciencias Matemat & Comp, Ave Trabalhador Sao Carlense 400, Ctr, BR-13566590 Sao Carlos, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B; v. 26, n. 3, p. 1653-1673, MAR 2021.
Web of Science Citations: 0

In this paper we study global dynamic aspects of the quadratic system (x) over dot = yz, (y) over dot = x - y, (z) over dot = 1 - x(alpha y + beta x), where (x, y, z) is an element of R-3 and alpha, beta is an element of {[}0, 1] are two parameters. It contains the Sprott B and the Sprott C systems at the two extremes of its parameter spectrum and we call it Sprott BC system. Here we present the complete description of its singularities and we show that this system passes through a Hopf bifurcation at alpha = 0. Using the Poincare compactification of a polynomial vector field in R-3 we give a complete description of its dynamic on the Poincare sphere at infinity. We also show that such a system does not admit a polynomial first integral, nor algebraic invariant surfaces, neither Darboux first integral. (AU)

FAPESP's process: 17/20854-5 - Qualitative theory of ordinary differential equations: integrability, periodic orbits and phase portraits
Grantee:Regilene Delazari dos Santos Oliveira
Support type: Regular Research Grants