Bifurcations at infinity, invariant algebraic surfaces, homoclinic and heteroclinic orbits and centers of a new Lorenz-like chaotic system

Author(s)

Gouveia, Marcio R. A. ^[1] ; Messias, Marcelo ^[2] ; Pessoa, Claudio ^[1]

Affiliation

^[1] Univ Estadual Paulista, Inst Biociencias Letras & Ciencias Exatas IBILCE, Dept Matemat, UNESP, Sao Jose Do Rio Preto, SP - Brazil

^[2] Univ Estadual Paulista, Dept Matemat & Comp, FCT, UNESP, Presidente Prudente, SP - Brazil

• Document type: Journal article
• Source: NONLINEAR DYNAMICS; v. 84, n. 2, p. 703-713, APR 2016.
• Web of Science Citations: 2

Abstract

We present a global dynamical analysis of the following quadratic differential system , where are the state variables and a, b, d, f, g are real parameters. This system has been proposed as a new type of chaotic system, having additional complex dynamical properties to the well-known chaotic systems defined in , alike Lorenz, Rossler, Chen and other. By using the Poincar, compactification for a polynomial vector field in , we study the dynamics of this system on the Poincar, ball, showing that it undergoes interesting types of bifurcations at infinity. We also investigate the existence of first integrals and study the dynamical behavior of the system on the invariant algebraic surfaces defined by these first integrals, showing the existence of families of homoclinic and heteroclinic orbits and centers contained on these invariant surfaces. (AU)

• FAPESP's process: 13/24541-0 - Ergodic and qualitative theory of dynamical systems
• Grantee: Claudio Aguinaldo Buzzi
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 12/18413-7 - Global analysis of polynomial differential systems defined on the space R3
• Grantee: Marcelo Messias
• Support Opportunities: Regular Research Grants