Dynamic aspects of Sprott BC chaotic system
type: Item
instance of: scholarly article
title: Dynamic aspects of Sprott BC chaotic system
zbMATH Open document ID: 1472.34073
author: Marcos C. Mota
author: Regilene Oliveira
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2021-06-04T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 34C45
zbMATH DE Number: 7355165
zbMATH Keywords: Sprott BC chaotic system
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: Poincaré compactification
zbMATH Keywords: invariant algebraic surfaces
zbMATH Keywords: Darboux integrability
reviewed by: Èduard V. Musafirov
MaRDI profile type: Publication
full work available at URL: dcdsb.2020177
OpenAlex ID: W3036002399
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DOI: 10.3934/DCDSB.2020177
description: scientific article; zbMATH DE number 7355165