Zero-zero-Hopf bifurcation and ultimate bound estimation of a generalized Lorenz-Stenflo hyperchaotic system

2016 ◽  
Vol 40 (10) ◽  
pp. 3424-3432 ◽  
Author(s):  
Yu-Ming Chen ◽  
Hai-Hua Liang
Keyword(s):  
Hopf Bifurcation ◽  
Hyperchaotic System ◽  
Ultimate Bound ◽  
Bound Estimation

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.

scholarly journals Dynamics of a New Hyperchaotic System with Only One Equilibrium Point

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xiang Li ◽  
Ranchao Wu
Keyword(s):  
Hopf Bifurcation ◽  
Hyperchaotic System ◽  
Compound Structure ◽  
Normal Form Theory ◽  
Controlled System ◽  
Forming Mechanism ◽  
Form Theory ◽  
The Lorenz System ◽  
The Stability ◽  
New Hyperchaotic System

A new 4D hyperchaotic system is constructed based on the Lorenz system. The compound structure and forming mechanism of the new hyperchaotic attractor are studied via a controlled system with constant controllers. Furthermore, it is found that the Hopf bifurcation occurs in this hyperchaotic system when the bifurcation parameter exceeds a critical value. The direction of the Hopf bifurcation as well as the stability of bifurcating periodic solutions is presented in detail by virtue of the normal form theory. Numerical simulations are given to illustrate and verify the results.

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