DYNAMIC ASPECTS OF SPROTT BC CHAOTIC SYSTEM

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.

Automated summary

This paper studies the quadratic system (x) over dot = yz, (y) over dot = x - y, (z) over dot = 1 - x(alpha y + beta x), and introduces the Sprott BC system. It analyzes the system's dynamics at different parameter values and demonstrates a Hopf bifurcation at α = 0.