Hopf bifurcation analysis and ultimate bound estimation of a new 4-D quadratic autonomous hyper-chaotic system

2016 ◽  
Vol 291 ◽  
pp. 323-339 ◽  
Author(s):  
Amin Zarei ◽  
Saeed Tavakoli
Keyword(s):  
Hopf Bifurcation ◽  
Chaotic System ◽  
Bifurcation Analysis ◽  
Ultimate Bound ◽  
Bound Estimation

Hopf bifurcation analysis and circuit implementation for a novel four-wing hyper-chaotic system

2013 ◽  
Vol 22 (8) ◽  
pp. 080504 ◽  
Author(s):  
Wei Xue ◽  
Guo-Yuan Qi ◽  
Jing-Jing Mu ◽  
Hong-Yan Jia ◽  
Yan-Ling Guo
Keyword(s):  
Hopf Bifurcation ◽  
Chaotic System ◽  
Bifurcation Analysis ◽  
Circuit Implementation

Local bifurcation analysis and ultimate bound of a novel 4D hyper-chaotic system

2014 ◽  
Vol 78 (4) ◽  
pp. 2517-2531 ◽  
Author(s):  
Jiezhi Wang ◽  
Qing Zhang ◽  
Zengqiang Chen ◽  
Hang Li
Keyword(s):  
Chaotic System ◽  
Bifurcation Analysis ◽  
Local Bifurcation ◽  
Local Bifurcation Analysis ◽  
Ultimate Bound

ULTIMATE BOUND ESTIMATION OF A CLASS OF HIGH DIMENSIONAL QUADRATIC AUTONOMOUS DYNAMICAL SYSTEMS

2011 ◽  
Vol 21 (09) ◽  
pp. 2679-2694 ◽  
Author(s):  
PEI WANG ◽  
DAMEI LI ◽  
XIAOQUN WU ◽  
JINHU LÜ ◽  
XINGHUO YU
Keyword(s):  
Dynamical Systems ◽  
Chaotic System ◽  
Lorenz System ◽  
High Dimensional ◽  
Hyperchaotic System ◽  
Sufficient Condition ◽  
System A ◽  
Ultimate Bound ◽  
Autonomous Dynamical Systems ◽  
Bound Estimation

This paper aims to propose a unified approach for the ultimate bound estimation of a class of High Dimensional Quadratic Autonomous Dynamical Systems (HDQADS). Using the proposed method and the optimization idea, a sufficient condition is then given for estimating the ultimate bounds of a class of HDQADS. To validate the above sufficient condition, this paper further investigates the ultimate bound estimation of a hyperchaotic system, a 6D and a 9D chaotic system, separately. Moreover, the ultimate bounds for a general Lorenz system, a low-order atmospheric circulation model, and a new 3D chaotic system are also discussed in detail. In particular, it should be pointed out that a unified and accurate ultimate bound estimation is attained for the generalized Lorenz system and it includes several well-known results as its special cases. Some numerical simulations are also given to verify and visualize the corresponding theoretical results.

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