Dynamic aspects of Sprott BC chaotic system
The authors consider the 3D system \begin{align*} & \dot{x}=yz, \\ & \dot{y}=x-y, \\ & \dot{z}=1-x\left( \alpha y+\beta x \right);\quad (x,y,z)\in {{\mathbb{R}}^{3}}, \\ \end{align*} where \(\alpha ,\beta \in [0,1]\) are system parameters. For \(\alpha =1\), \(\beta =0\), the considered system coincides with the Sprott B chaotic system and for \(\alpha =0\), \(\beta =1\), it coincides with the Sprott C chaotic system. It is shown that the considered system has two unstable equilibrium points. Further, the authors prove that this system passes through a subcritical Hopf bifurcation at \(\alpha =0\). The Poincaré compactification for a polynomial vector field is used for studying the behavior of the system at infinity. Moreover, it is proved that the system does not possess a polynomial first integral, nor algebraic invariant surfaces, neither a Darboux first integral.
scientific article; zbMATH DE number 7355165