scholarly journals Controlling Hyper Chaos with Feedback of Dynamical Variables

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4272-4277 ◽  
Author(s):  
Xiao-Shu Luo ◽  
Bing-Hong Wang
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Theoretical Analysis ◽  
Chaotic Attractors ◽  
Chaotic Circuit ◽  
Controlled System ◽  
Controlling Chaos ◽  
Simulation Results ◽  
System Variables ◽  
Proportional Feedback

We propose a method for controlling chaos and hyper-chaos by applying continuous proportional feedback to the system variables and their derivatives. The method has been applied successfully in six-order coupled Chua's hyper-chaotic circuit system. The theoretical analysis and numerical simulation results show that unstable fixed points embedded in hyper-chaotic attractors can be stabilized and Hopf bifurcation can be observed for the controlled system.

scholarly journals Low Model Analysis and Synchronous Simulation of the Wave Mechanics

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Wenyuan Duan ◽  
Heyuan Wang ◽  
Meng Kan
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Chaotic System ◽  
Invariant Set ◽  
Positive Definite ◽  
Chaotic Attractors ◽  
Wave Mechanics ◽  
Wave Dynamics ◽  
Simulation Results ◽  
Positive Invariant Set

The dynamic behavior of a chaotic system in the internal wave dynamics and the problem of the tracing and synchronization are investigated, and the numerical simulation is carried out in this paper. The globally exponentially attractive set and positive invariant set of the chaotic system are studied via constructing the positive definite and radial unbounded Lyapunov function. There are no equilibrium positions, periodic solutions, quasi-period motions, wandering recovering motions, and other chaotic attractors of the system out of the globally exponentially attractive set. Strange attractors can only locate in the globally exponentially attractive set. A feedback controller is designed for the chaotic system to realize the control of the unstable point. The second method of Lyapunov is used to discuss theoretically the rationality of the design of the controller. The driving-response synchronization method is used to realize the globally exponential synchronization. The numerical simulation is carried out by MATLAB software, and the simulation results show that the method is effective.

scholarly journals A Novel 2D – Grid of Scroll Chaotic Attractor Generated by CNN

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 99 ◽  
Author(s):  
Ahmed M. Ali ◽  
Saif M. Ramadhan ◽  
Fadhil R. Tahir
Keyword(s):  
Theoretical Analysis ◽  
Chaotic Attractor ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Chaotic Attractors ◽  
Electronic Circuits ◽  
Nonlinear Networks ◽  
Design And Implementation ◽  
Simulation Results ◽  
New System

The complex grid of scroll chaotic attractors that are generated through nonlinear electronic circuits have been raised considerably over the last decades. In this paper, it is shown that a subclass of Cellular Nonlinear Networks (CNNs) allows us to generate complex dynamics and chaos in symmetry pattern. A novel grid of scroll chaotic attractor, based on a new system, shows symmetry scrolls about the origin. Also, the equilibrium points are located in a manner such that the symmetry about the line x=y has been achieved. The complex dynamics of system can be generated using CNNs, which in turn are derived from a CNN array (1×3) cells. The paper concerns on the design and implementation of 2×2 and 3×3 2D-grid of scroll via the CNN model. Theoretical analysis and numerical simulations of the derived model are included. The simulation results reveal that the grid of scroll attractors can be successfully reproduced using PSpice.

scholarly journals Hopf Bifurcation and Chaos of a Delayed Finance System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Xuebing Zhang ◽  
Honglan Zhu
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Center Manifold ◽  
Chaotic State ◽  
Bifurcation And Chaos ◽  
Finance System ◽  
Center Manifold Theorem ◽  
Normal Form Method ◽  
Simulation Results ◽  
The Stability

In this paper, a finance system with delay is considered. By analyzing the corresponding characteristic equations, the local stability of equilibrium is established. The existence of Hopf bifurcations at the equilibrium is also discussed. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis. Numerical simulation results show that delay can lead a stable system into a chaotic state.

A New Multi-Scroll Chaotic Attractors Synchronization Technique

2012 ◽  
Vol 220-223 ◽  
pp. 1226-1229 ◽  
Author(s):  
Dan Li ◽  
Lu Wang
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Chaotic Attractors ◽  
Dimensional System

Multi-scroll chaotic attractors synchronization technique is a research focuses in recent years. This paper focuses on multi-scroll chaotic attractors in the four-dimensional system. It uses variable feedback synchronous method and active-passive synchronous method to achieve the two 6-scroll chaotic attractors’ synchronization. The feasibility of this method is proved by theoretical analysis and numerical simulation. Simultaneously, it gets a better synchronization results.

Design of Grid Multiscroll Chaotic Attractors via Transformations

2015 ◽  
Vol 25 (10) ◽  
pp. 1530027 ◽  
Author(s):  
Xingxing Ai ◽  
Kehui Sun ◽  
Shaobo He ◽  
Huihai Wang
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Exponent ◽  
Theoretical Analysis ◽  
Experimental Verification ◽  
Equilibrium Points ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
Largest Lyapunov Exponent ◽  
One Dimensional ◽  
Circular Grid

Three transformation approaches for generating grid multiscroll chaotic attractors are presented through theoretical analysis and numerical simulation. Three kinds of grid multiscroll chaotic attractors are generated based on one-dimensional multiscroll Chua system. The dynamics of the multiscroll chaotic attractors are analyzed by means of equilibrium points, eigenvalues, the largest Lyapunov exponent and complexity. As the experimental verification, we implemented the circular grid multiscroll attractor on DSP platform. The simulation and experimental results are consistent well with that of theoretical analysis, and it shows that the design approaches are effective.

scholarly journals A Meminductor-based Chaotic System

2020 ◽  
Vol 49 (2) ◽  
pp. 317-332
Author(s):  
Aixue Qi ◽  
Lei Ding ◽  
Wenbo Liu
Keyword(s):  
Theoretical Analysis ◽  
Chaotic System ◽  
Phase Trajectory ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Circuit Parameter ◽  
Bifurcation Diagrams ◽  
Dynamical Behaviors ◽  
Simulation Results

We propose a meminductor-based chaotic system. Theoretical analysis and numerical simulations reveal complex dynamical behaviors of the proposed meminductor-based chaotic system with five unstable equilibrium points and three different states of chaotic attractors in its phase trajectory with only a single change in circuit parameter. Lyapunov exponents, bifurcation diagrams, and phase portraits are used to investigate its complex chaotic and multi-stability behaviors, including its coexisting chaotic, periodic and point attractors. The proposed meminductor-based chaotic system was implemented using analog integrators, inverters, summers, and multipliers. PSPICE simulation results verified different chaotic characteristics of the proposed circuit with a single change in a resistor value.

Numerical Simulation of Air-Deck Slotted Charge Blasting

2010 ◽  
Vol 143-144 ◽  
pp. 787-791 ◽  
Author(s):  
Guo Liang Yang ◽  
Ren Shu Yang ◽  
Chuan Huo ◽  
Y.L. Che
Keyword(s):  
Numerical Simulation ◽  
Stress Distribution ◽  
Theoretical Analysis ◽  
Physical Process ◽  
Laboratory Tests ◽  
Decisive Role ◽  
Simulation Method ◽  
Numerical Simulation Method ◽  
Simulation Results ◽  
Air Deck

Air-deck ratio plays a decisive role in blasting engineering. Researchers have conducted extensive work to study the optimal air-deck ratio. But consensus has not been achieved. Especially slotted charge blasting, the study on it just starts. For its complicated physical process in blasting, it is difficult to perform theoretical analysis to obtain the law between blasting result and air-deck ratio. The numerical simulation method is adopted to study the effect of different air-deck ratio on stress distribution at first. And then laboratory tests are carried out to validate the simulation results. The conclusion may be drawn that good directional fracture could be obtained with air-deck ratio 33.3% ~ 50%. The achievement could provide reference for blasting engineering.

scholarly journals Multiconsensus of Second-Order Multiagent Systems with Input Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Jie Chen ◽  
Ming Chi ◽  
Zhi-Hong Guan ◽  
Rui-Quan Liao ◽  
Ding-Xue Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Theoretical Analysis ◽  
Multiagent Systems ◽  
Upper Bound ◽  
Multiagent System ◽  
Second Order ◽  
Matrix Analysis ◽  
Simulation Results ◽  
Input Delays ◽  
Double Integrator

The multiconsensus problem of double-integrator dynamic multiagent systems has been investigated. Firstly, the dynamic multiconsensus, the static multiconsensus, and the periodic multiconsensus are considered as three cases of multiconsensus, respectively, in which the final multiconsensus convergence states are established by using matrix analysis. Secondly, as for the multiagent system with input delays, the maximal allowable upper bound of the delays is obtained by employing Hopf bifurcation of delayed networks theory. Finally, simulation results are presented to verify the theoretical analysis.

Achieving the Multi-Scroll Chaotic Attractors’ Synchronization in the Four-Dimensional System by Driving-Response Synchronization Method

2014 ◽  
Vol 635-637 ◽  
pp. 1076-1080
Author(s):  
Dan Li ◽  
Meng Jin ◽  
Zhen Fan ◽  
Xian Da Dong
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Chaotic Attractors ◽  
Dimensional System ◽  
Important Research ◽  
Synchronization Method

Multi-scroll chaotic attractors’ synchronization technology is one of the important research achievements in recent years.This paper uses driving-response synchronization method to achieve the two 6-scroll chaotic attractors’ synchronization in the four-dimensional syetem.The feasibility of this method is proved by theoretical analysis and numerical simulation.

A SIMPLE MEMRISTOR CHAOTIC CIRCUIT WITH COMPLEX DYNAMICS

2011 ◽  
Vol 21 (09) ◽  
pp. 2629-2645 ◽  
Author(s):  
BOCHENG BAO ◽  
ZHENGHUA MA ◽  
JIANPING XU ◽  
ZHONG LIU ◽  
QIANG XU
Keyword(s):  
Numerical Simulation ◽  
Finite Time ◽  
Complex Dynamics ◽  
Circuit Implementation ◽  
Chaotic Circuit ◽  
Cubic Nonlinearity ◽  
Initial State ◽  
Simulation Results ◽  
Active Flux ◽  
Different Time Scales

A simple memristor-based chaotic circuit with an active flux-controlled memristor characterized by a smooth continuous cubic nonlinearity is designed. The proposed chaotic circuit can generate a 2-scroll chaotic attractor on a finite time scale and has an equilibrium set with its stability dependent on the initial state of the memristor. The complex dynamics of the proposed chaotic circuit under different initial state of the memristor are investigated both theoretically and numerically. In particular, some novel transient transition behaviors with different time scales are found in the memristor circuit. Experimental observations based on a universal circuit implementation platform are conducted to partially verify the numerical simulation results.

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