scholarly journals Synchronization of a Hyperchaotic Finance System

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Huangen Chen ◽  
Lu Yu ◽  
Yilin Wang ◽  
Miaomei Guo
Keyword(s):  
Numerical Methods ◽  
Chaotic Systems ◽  
Control Strategies ◽  
Exponential Synchronization ◽  
Financial Systems ◽  
Finance System ◽  
Mathematical Proofs ◽  
Initial Values ◽  
Two Systems ◽  
Asymptotic Synchronization

In this article, we propose a series of control strategies to synchronize two chaotic financial systems. Due to the characteristics of chaotic systems, the system is very sensitive to its initial values. Thus, the behaviour of two systems with different initial values will be completely different. In order to realize the synchronization of two financial chaotic systems, we designed a series of controls including controllers to realize global asymptotic synchronization and controllers to realize global exponential synchronization to make the two systems fully synchronized. We provide mathematical proofs to show that the designed controls are effective. Numerical methods are used to verify the effectiveness of the controls.

MUTUAL AND SELF-COMPOUNDING OF CHAOTIC SYSTEMS

1996 ◽  
Vol 06 (04) ◽  
pp. 759-767
Author(s):  
R. SINGH ◽  
P.S. MOHARIR ◽  
V.M. MARU
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Dynamic Systems ◽  
Mantle Convection ◽  
Chaotic Systems ◽  
Compound System ◽  
Two Systems

The notion of compounding a chaotic system was introduced earlier. It consisted of varying the parameters of the compoundee system in proportion to the variables of the compounder system, resulting in a compound system which has in general higher Lyapunov exponents. Here, the notion is extended to self-compounding of a system with a real-earth example, and mutual compounding of dynamic systems. In the former, the variables in a system perturb its parameters. In the latter, two systems affect the parameters of each other in proportion to their variables. Examples of systems in such compounding relationships are studied. The existence of self-compounding is indicated in the geodynamics of mantle convection. The effect of mutual compounding is studied in terms of Lyapunov exponent variations.

scholarly journals Design of a Nonhomogeneous Nonlinear Synchronizer and Its Implementation in Reconfigurable Hardware

2020 ◽  
Vol 25 (3) ◽  
pp. 51
Author(s):  
Jesus R. Pulido-Luna ◽  
Jorge A. López-Rentería ◽  
Nohe R. Cazarez-Castro
Keyword(s):  
Asymptotic Stability ◽  
Test Performance ◽  
State Feedback ◽  
Chaotic Systems ◽  
Reconfigurable Hardware ◽  
Lyapunov Theory ◽  
Control Law ◽  
Heterogeneous Dynamics ◽  
Two Systems ◽  
Error State

In this work, a generalization of a synchronization methodology applied to a pair of chaotic systems with heterogeneous dynamics is given. The proposed control law is designed using the error state feedback and Lyapunov theory to guarantee asymptotic stability. The control law is used to synchronize two systems with different number of scrolls in their dynamics and defined in a different number of pieces. The proposed control law is implemented in an FPGA in order to test performance of the synchronization schemes.

scholarly journals Finite Time Stability of Finance Systems with or without Market Confidence Using Less Control Input

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Chao Ma ◽  
Yujuan Tian ◽  
Zhongfeng Qu
Keyword(s):  
Finite Time ◽  
Chaotic Systems ◽  
Control Method ◽  
Control Input ◽  
Three Dimension ◽  
Time Stability ◽  
Finance System ◽  
Finite Time Stability ◽  
Single Controller ◽  
Simulation Results

In this paper, we make an exploration of a technique to control a class of finance chaotic systems. This technique allows one to achieve the finite time stability of the finance system more effectively with less control input energy. First, the finite time stability of three dimension finance system without market confidence is analyzed by using a single controller. Then, two controllers are designed to stabilize the four-dimension finance system with market confidence. Moreover, the finite time stability of the three-dimension and four-dimension finance system with unknown parameter is also studied. Finally, simulation results are presented to show the chaotic behaviour of the finance systems, verify the effectiveness of the proposed control method, and illustrate its advantages compared with other methods.

ON ADAPTIVE SYNCHRONIZATION AND CONTROL OF NONLINEAR DYNAMICAL SYSTEMS

1996 ◽  
Vol 06 (03) ◽  
pp. 455-471 ◽  
Author(s):  
CHAI WAH WU ◽  
TAO YANG ◽  
LEON O. CHUA
Keyword(s):  
Spread Spectrum ◽  
Communication Systems ◽  
Chaotic Systems ◽  
Nonlinear Dynamical Systems ◽  
Adaptive Synchronization ◽  
Adaptive Controllers ◽  
Nonlinear Dynamical ◽  
Two Systems ◽  
And Control

In this paper, we study the synchronization of two coupled nonlinear, in particular chaotic, systems which are not identical. We show how adaptive controllers can be used to adjust the parameters of the systems such that the two systems will synchronize. We use a Lyapunov function approach to prove a global result which shows that our choice of controllers will synchronize the two systems. We show how it is related to Huberman-Lumer adaptive control and the LMS adaptive algorithm. We illustrate the applicability of this method using Chua's oscillators as the chaotic systems. We choose parameters for the two systems which are orders of magnitude apart to illustrate the effectiveness of the adaptive controllers. Finally, we discuss the role of adaptive synchronization in the context of secure and spread spectrum communication systems. In particular, we show how several signals can be encoded onto a single scalar chaotic carrier signal.

SYNCHRONIZATION OF UNCERTAIN HYPERCHAOTIC AND CHAOTIC SYSTEMS BY ADAPTIVE CONTROL

2008 ◽  
Vol 18 (12) ◽  
pp. 3731-3736 ◽  
Author(s):  
ZHI-YU LIU ◽  
CHIA-JU LIU ◽  
MING-CHUNG HO ◽  
YAO-CHEN HUNG ◽  
TZU-FANG HSU ◽  
...  
Keyword(s):  
Chaotic Systems ◽  
Mean Squared Error ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Slave System ◽  
Unknown Parameters ◽  
Squared Error ◽  
Master System ◽  
Two Systems ◽  
The Mean

This paper presents the synchronization between uncertain hyperchaotic and chaotic systems. Based on Lyapunov stability theory, an adaptive controller is derived to achieve synchronization of hyperchaotic and chaotic systems, including the case of unknown parameters in these two systems. The T.N.Č. hyperchaotic oscillator is used as the master system, and the Rössler system is used as the slave system. Numerical simulations verify these results. Additionally, the effect of noise is investigated by measuring the mean squared error (MSE) of two systems.

CONTROL STRATEGIES FOR CHAOTIC NEUROMODULES

1996 ◽  
Vol 06 (04) ◽  
pp. 693-703 ◽  
Author(s):  
NICO STOLLENWERK ◽  
FRANK PASEMANN
Keyword(s):  
Least Squares ◽  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Least Squares Method ◽  
Control Strategies ◽  
Nonlinear Least Squares ◽  
The Neural Network ◽  
One Step ◽  
Nonlinear Least Squares Method ◽  
The One

Different strategies for control of chaotic systems are discussed: The well known Ott-Grebogi-Yorke algorithm and two alternative algorithms based on least-squares minimisation of the one step future deviation. To compare their effectiveness in the neural network context they are applied to a minimal two neuron module with discrete chaotic dynamics. The best method with respect to calculation effort, to neural implementation, and to controlling properties is the nonlinear least squares method. Furthermore, it is observed in simulations that one can stabilise a whole periodic orbit by applying the control signals only to one of its periodic points, which lies in a distinguished region of phase space.

Sign in / Sign up

Export Citation Format

Share Document