GENERATING CHAOS VIA A DYNAMICAL CONTROLLER

2001 ◽  
Vol 11 (03) ◽  
pp. 865-869 ◽  
Author(s):  
GUO-QUN ZHONG ◽  
KIM F. MAN ◽  
GUANRONG CHEN
Keyword(s):  
Computer Simulation ◽  
Autonomous System ◽  
Quadratic Function ◽  
Feedback Controller ◽  
Nonlinear Feedback ◽  
Circuit Implementation ◽  
Linear Autonomous System

This Letter studies the generation of chaos from a linear autonomous system by employing a dynamical nonlinear feedback controller. The system setup is quite simple, and the only nonlinearity is a piecewise-quadratic function in the form of x|x|. Both computer simulation and circuit implementation are given to verify the chaos generated by this mechanism.

DESIGN AND CIRCUIT IMPLEMENTATION OF FRACTIONAL-ORDER MULTIWING CHAOTIC ATTRACTORS

2012 ◽  
Vol 22 (11) ◽  
pp. 1250269 ◽  
Author(s):  
ZILONG TANG ◽  
CHAOXIA ZHANG ◽  
SIMIN YU
Keyword(s):  
Fractional Order ◽  
Differential System ◽  
State Feedback ◽  
Quadratic Function ◽  
Feedback Controller ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
Novel Approach ◽  
Linear Differential ◽  
Nonlinear State

In this paper, a novel approach is proposed for generating fractional-order multiwing chaotic attractors. Based on a fractional-order linear differential system, by introducing the nonlinear state feedback controller equipped with an even symmetric multisegment quadratic function, various fractional-order multiwing chaotic attractors can be generated. An improved module-based circuit is also designed for verifying the effectiveness of the proposed method.

GENERATING 3-D SCROLL GRID ATTRACTORS OF FRACTIONAL DIFFERENTIAL SYSTEMS VIA STAIR FUNCTION

2007 ◽  
Vol 17 (11) ◽  
pp. 3965-3983 ◽  
Author(s):  
WEIHUA DENG
Keyword(s):  
Differential System ◽  
Autonomous System ◽  
Function Approach ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential System ◽  
Linear Autonomous System ◽  
Fractional Differential ◽  
The One ◽  
Number Of Equilibria

This paper discusses the stair function approach for the generation of scroll grid attractors of fractional differential systems. The one-directional (1-D) n-grid scroll, two-directional (2-D) (n × m)-grid scroll and three-directional (3-D) (n × m × l)-grid scroll attractors are created from a fractional linear autonomous system with a simple stair function controller. Being similar to the scroll grid attractors of classical differential systems, the scrolls of 1-D n-grid scroll, 2-D (n × m)-grid scroll and 3-D (n × m × l)-grid scroll attractors are located around the equilibria of fractional differential system on a line, on a plane or in 3D, respectively and the number of scrolls is equal to the corresponding number of equilibria.

scholarly journals Nonlinear feedback controller for the synchronization of (chaotic) systems with known parameters

2020 ◽  
Vol 23 (02) ◽  
pp. 124-135
Author(s):  
Muhammad Haris ◽  
Muhammad Shafiq ◽  
Adyda Ibrahim ◽  
Masnita Misiran
Keyword(s):  
Closed Loop ◽  
Lyapunov Stability Theory ◽  
Feedback Controller ◽  
Control Signal ◽  
Stability And Convergence ◽  
Nonlinear Feedback ◽  
Nonlinear Part ◽  
Synchronization Errors ◽  
Novel Structure ◽  
Linear And Nonlinear

This paper proposes, designs, and analyses a novel nonlinear feedback controller that realizes fast, and oscillation free convergence of the synchronization error to the equilibrium point. Oscillation free convergence lowers the failure chances of a closed-loop system due to the reduced chattering phenomenon in the actuator motion, which is a consequence of low energy sm ooth control signal. The proposed controller has a novel structure. This controller does not cancel nonlinear terms of the plant in the closed-loop; this attribute improves the robustness of the loop. The controller consists of linear and nonlinear parts; each part executes a specific task. The linear term in the controller keeps the closed-loop stable, while the nonlinear part of the controller facilitates the fast convergence of the error signal to the vicinity of the origin. Then the linear controller synthesizes a smooth control signal that moves the error signals to zero without oscillations. The nonlinear term of the controller does not contribute to this synthesis. The collaborative combination of linear and nonlinear controllers that drive the synchronization errors to zero is innovative. The paper establishes proof of global stability and convergence behavior by describing a detailed analysis based on the Lyapunov stability theory. Computer simulation results of two numerical examples verify the performance of the proposed controller approach. The paper also provides a comparative study with state-of-the-art controllers.

Stochastic synchronization of complex networks via a novel adaptive composite nonlinear feedback controller

2014 ◽  
Vol 80 (1-2) ◽  
pp. 363-374 ◽  
Author(s):  
Weiping Wang ◽  
Lixiang Li ◽  
Haipeng Peng ◽  
Jürgen Kurths ◽  
Jinghua Xiao ◽  
...  
Keyword(s):  
Complex Networks ◽  
Feedback Controller ◽  
Nonlinear Feedback ◽  
Composite Nonlinear Feedback ◽  
Stochastic Synchronization ◽  
Adaptive Composite

scholarly journals Rendering a subcritical Hopf bifurcation supercritical

1996 ◽  
Vol 317 ◽  
pp. 91-109 ◽  
Author(s):  
Po Ki Yuen ◽  
Haim H. Bau
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycle ◽  
Thermal Convection ◽  
Control Strategy ◽  
Chaotic Motion ◽  
Feedback Controller ◽  
Nonlinear Feedback ◽  
Naturally Occurring ◽  
Subcritical Hopf Bifurcation ◽  
Stable Periodic

It is demonstrated experimentally and theoretically that through the use of a nonlinear feedback controller, one can render a subcritical Hopf bifurcation supercritical and thus dramatically modify the nature of the flow in a thermal convection loop heated from below and cooled from above. In particular, we show that the controller can replace the naturally occurring chaotic motion with a stable, periodic limit cycle. The control strategy consists of sensing the deviation of fluid temperatures from desired values at a number of locations inside the loop and then altering the wall heating to counteract such deviations.

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