A New Six-Term 3D Unified Chaotic System

2020 ◽  
Vol 44 (4) ◽  
pp. 1593-1604
Author(s):  
Engin Can ◽  
Uğur Erkin Kocamaz ◽  
Yılmaz Uyaroğlu
Keyword(s):  
Chaotic System ◽  
Unified Chaotic System

A Unified Chaotic System with Various Coexisting Attractors

2021 ◽  
Vol 31 (01) ◽  
pp. 2150013
Author(s):  
Qiang Lai
Keyword(s):  
Chaotic System ◽  
Equilibrium Points ◽  
Sine Function ◽  
Coexisting Attractors ◽  
Dynamic Behaviors ◽  
Multiple Zeros ◽  
Unified Chaotic System

This article presents a unified four-dimensional autonomous chaotic system with various coexisting attractors. The dynamic behaviors of the system are determined by its special nonlinearities with multiple zeros. Two cases of nonlinearities with sine function of the system are discussed. The symmetrical coexisting attractors, asymmetrical coexisting attractors and infinitely many coexisting attractors in the system are numerically demonstrated. This shows that such a system has an ability to produce abundant coexisting attractors, depending on the number of equilibrium points determined by nonlinearities.

scholarly journals On the Dynamics of the Unified Chaotic System Between Lorenz and Chen Systems

2015 ◽  
Vol 25 (09) ◽  
pp. 1550122 ◽  
Author(s):  
Jaume Llibre ◽  
Ana Rodrigues
Keyword(s):  
Chaotic System ◽  
Parameter Family ◽  
Algebraic Surfaces ◽  
Hopf Bifurcations ◽  
Global Dynamics ◽  
Differential Systems ◽  
Special Values ◽  
Unified Chaotic System ◽  
Invariant Algebraic Surfaces ◽  
The Family

A one-parameter family of differential systems that bridges the gap between the Lorenz and the Chen systems was proposed by Lu, Chen, Cheng and Celikovsy. The goal of this paper is to analyze what we can say using analytic tools about the dynamics of this one-parameter family of differential systems. We shall describe its global dynamics at infinity, and for two special values of the parameter a we can also describe the global dynamics in the whole ℝ3using the invariant algebraic surfaces of the family. Additionally we characterize the Hopf bifurcations of this family.

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