Coexistence of chaotic attractor and unstable limit cycles in a 3D dynamical system

Dana Constantinescu; Gheorghe Tigan; Xiang Zhang

doi:10.12688/openreseurope.13590.1

Coexistence of chaotic attractor and unstable limit cycles in a 3D dynamical system

Open Res Eur. 2021 May 17:1:50. doi: 10.12688/openreseurope.13590.1. eCollection 2021.

Authors

Dana Constantinescu¹, Gheorghe Tigan², Xiang Zhang³

Affiliations

¹ Department of Applied Mathematics, University of Craiova, Craiova, 200585, Romania.
² Department of Mathematics, Politehnica University of Timisoara, Timisoara, 300006, Romania.
³ School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China.

Abstract

The coexistence of stable limit cycles and chaotic attractors has already been observed in some 3D dynamical systems. In this paper we show, using the T-system, that unstable limit cycles and chaotic attractors can also coexist. Moreover, by completing the characterization of the existence of invariant algebraic surfaces and their associated global dynamics, we give a better understanding on the disappearance of the strange attractor and the limit cycles of the studied system.

Keywords: algebraic invariant surfaces; bifurcation; chaotic attractors; global dynamics; limit cycle.

Grants and funding

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No [777911], (project Dynamics). XZ is partially supported by the National Social Science Fund of China, grant number 11871334.