Optimal Control and Synchronization of Alternated Julia Sets

2015 ◽  
Vol 18 (5) ◽  
pp. 1698-1705 ◽  
Author(s):  
Pei Wang ◽  
Shutang Liu
Keyword(s):  
Optimal Control ◽  
Julia Sets ◽  
Control And Synchronization

CONTROL AND SYNCHRONIZATION OF JULIA SETS OF THE COMPLEX PERTURBED RATIONAL MAPS

2013 ◽  
Vol 23 (05) ◽  
pp. 1350083 ◽  
Author(s):  
YONGPING ZHANG
Keyword(s):  
Optimal Control ◽  
Function Method ◽  
Control Method ◽  
Control Function ◽  
Julia Set ◽  
Julia Sets ◽  
Rational Maps ◽  
Control And Synchronization ◽  
Function Synchronization ◽  
Optimal Control Function

The dynamical and fractal behaviors of the complex perturbed rational maps [Formula: see text] are discussed in this paper. And the optimal control function method is taken on the Julia set of this system. In this control method, infinity is regarded as a fixed point to be controlled. By substituting the driving item for an item in the optimal control function, synchronization of Julia sets of two such different systems is also studied.

scholarly journals Impulsive Control and Synchronization of Complex Lorenz Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Shaban Aly ◽  
Ali Al-Qahtani ◽  
Houari B. Khenous ◽  
Gamal M. Mahmoud
Keyword(s):  
Optimal Control ◽  
Population Dynamics ◽  
Nonlinear Systems ◽  
Real World ◽  
Global Exponential Stability ◽  
Impulsive Control ◽  
Biological Phenomena ◽  
Control And Synchronization ◽  
Natural Description ◽  
Real World Problems

In this paper, we continue our investigations on control and synchronization of the complex Lorenz systems by investigating impulsive control and synchronization. Nonlinear systems involving impulse effects, appear as a natural description of observed evolution phenomena of several real world problems; For example, many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, population dynamics and so forth do exhibit impulsive effects. Some new and more comprehensive criteria for global exponential stability and asymptotical stability of impulsively controlled complex Lorenz systems are established with varying impulsive intervals. The effectiveness of the proposed technique is verified through numerical simulations.

scholarly journals Control and synchronization of Julia sets of the complex dissipative standard system

2016 ◽  
Vol 21 (4) ◽  
pp. 465-476
Author(s):  
Weihua Sun ◽  
Yongping Zhang
Keyword(s):  
Control Parameter ◽  
Julia Set ◽  
Julia Sets ◽  
The Other ◽  
Standard System ◽  
Control And Synchronization ◽  
Backward Orbits

The fractal behaviors of the complex dissipative standard system are discussed in this paper. By using the boundedness of the forward and backward orbits, Julia set of the system is introduced and visualization of Julia set is also given. Then a controller is designed to achieve Julia set shrinking or expanding with the changing of the control parameter. And synchronization of two different Julia sets is discussed by adding a coupling item, which makes one Julia set change to be the other. The simulations illustrate the efficacy of these methods.

Gradient control and synchronization of Julia sets

2008 ◽  
Vol 17 (2) ◽  
pp. 543-549 ◽  
Author(s):  
Zhang Yong-Ping ◽  
Liu Shu-Tang
Keyword(s):  
Julia Sets ◽  
Gradient Control ◽  
Control And Synchronization
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