GENERALIZED SYNCHRONIZATION IN DOUBLY DRIVEN CHAOTIC SYSTEM

2006 ◽  
Vol 20 (24) ◽  
pp. 3477-3485
Author(s):  
XIA HUANG ◽  
JIAN GAO ◽  
DAIHAI HE ◽  
ZHIGANG ZHENG
Keyword(s):  
Chaotic System ◽  
Conditional Entropy ◽  
Chaotic Oscillator ◽  
Generalized Synchronization ◽  
Entropy Analysis ◽  
Entropy Spectrum ◽  
Chaotic Signals ◽  
Coupling Strengths ◽  
Conventional Methods ◽  
Parameter Values

Generalized synchronization (GS) of a chaotic oscillator driven by two chaotic signals is investigated in this paper. Both receiver and drivers are the same kind of oscillators with mismatched parameter values. Partial and global GS may appear depending on coupling strengths. An approach based on the conditional entropy analysis is presented to test the partial GS, which is difficult to determine with conventional methods. A trough in conditional entropy spectrum indicates partial GS between the receiver and one of the drivers.

A Switchable Chaotic Oscillator with Two Amplitude–Frequency Controllers

2017 ◽  
Vol 26 (10) ◽  
pp. 1750158 ◽  
Author(s):  
Wen Hu ◽  
Akif Akgul ◽  
Chunbiao Li ◽  
Taicheng Zheng ◽  
Peng Li
Keyword(s):  
Chaotic System ◽  
Value Function ◽  
Chaotic Signal ◽  
Signal Generator ◽  
Chaotic Oscillator ◽  
Absolute Value ◽  
Independent Amplitude ◽  
Chaotic Signals ◽  
Chaotic Signal Generator ◽  
Frequency Controller

A simple chaotic system with a single nonquadratic term is developed to be a switchable chaotic signal generator in this paper. Additional nonlinearity of the absolute value function is introduced for reforming the structure without damaging the basic dynamics but yielding a new independent amplitude–frequency controller. A switchable chaotic experimental oscillator is designed afterwards, where two coefficients corresponding to two independent rheostats rescale the amplitude and frequency of the chaotic signals smoothly. To our knowledge, this has never been found in other chaotic oscillators.

A Compact and Low Power Realization of a High Frequency Chaotic Oscillator

2017 ◽  
Vol 2017 (DPC) ◽  
pp. 1-27
Author(s):  
R. Chase Harrison ◽  
Benjamin K. Rhea ◽  
Frank T. Werner ◽  
Robert N. Dean
Keyword(s):  
Low Power ◽  
Chaotic System ◽  
High Frequency ◽  
High Speed ◽  
Random Number ◽  
Nonlinear Dynamical Systems ◽  
Initial Conditions ◽  
Random Number Generation ◽  
Chaotic Oscillator ◽  
Number Generation

The desirable properties exhibited in some nonlinear dynamical systems have many potential uses. These properties include sensitivity to initial conditions, wide bandwidth, and long-term aperiodicity, which lend themselves to applications such as random number generation, communication and audio ranging systems. Chaotic systems can be realized in electronics by using inexpensive and readily available parts. Many of these systems have been verified in electronics using nonpermanent prototyping at very low frequencies; however, this restricts the range of potential applications. In particular, random number generation (RNG) benefits from an increase in operation frequency, since it is proportional to the amount of bits that can be produced per second. This work looks specifically at the nonlinear element in the chaotic system and evaluates its frequency limitations in electronics. In practice, many of nonlinearities are difficult to implement in high speed electronics. In addition to this restriction, the use of complex feedback paths and large inductors prevents the miniaturization that is desirable for implementing chaotic circuits in other electronic systems. By carefully analyzing the fundamental dynamics that govern the chaotic system, these problems can be addressed. Presented in this work is the design and realization of a high frequency chaotic oscillator that exhibits complex and rich dynamics while using a compact footprint and low power consumption.

Impulsive generalized synchronization of chaotic system

2007 ◽  
Vol 16 (7) ◽  
pp. 1912-1917 ◽  
Author(s):  
Zhang Rong ◽  
Xu Zhen-Yuan ◽  
He Xue-Ming
Keyword(s):  
Chaotic System ◽  
Generalized Synchronization

A Modified Multistable Chaotic Oscillator

2018 ◽  
Vol 28 (07) ◽  
pp. 1850085 ◽  
Author(s):  
Zhouchao Wei ◽  
Viet-Thanh Pham ◽  
Abdul Jalil M. Khalaf ◽  
Jacques Kengne ◽  
Sajad Jafari
Keyword(s):  
Chaotic System ◽  
Limit Cycles ◽  
Initial Conditions ◽  
Chaotic Oscillator ◽  
Two Dimensional ◽  
Different Types ◽  
New System

In this paper, by modifying a known two-dimensional oscillator, we obtain an interesting new oscillator with coexisting limit cycles and point attractors. Then by changing this new system to its forced version and choosing a proper set of parameters, we introduce a chaotic system with some very interesting features. In this system, not only can we see the coexistence of different types of attractors, but also a fascinating phenomenon: some initial conditions can escape from the gravity of nearby attractors and travel far away before being trapped in an attractor beyond the usual access.

The Effects of a Constant Excitation Force on the Dynamics of an Infinite-Equilibrium Chaotic System Without Linear Terms: Analysis, Control and Circuit Simulation

2020 ◽  
Vol 30 (15) ◽  
pp. 2050234
Author(s):  
L. Kamdjeu Kengne ◽  
Z. Tabekoueng Njitacke ◽  
J. R. Mboupda Pone ◽  
H. T. Kamdem Tagne
Keyword(s):  
Chaotic System ◽  
Analog Circuit ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Nonlinear Behavior ◽  
Basins Of Attraction ◽  
Phase Portraits ◽  
Unique Contribution ◽  
Chaotic Signals ◽  
Excitation Force

In this paper, the effects of a bias term modeling a constant excitation force on the dynamics of an infinite-equilibrium chaotic system without linear terms are investigated. As a result, it is found that the bias term reduces the number of equilibrium points (transition from infinite-equilibria to only two equilibria) and breaks the symmetry of the model. The nonlinear behavior of the system is highlighted in terms of bifurcation diagrams, maximal Lyapunov exponent plots, phase portraits, and basins of attraction. Some interesting phenomena are found including, for instance, hysteretic dynamics, multistability, and coexisting bifurcation branches when monitoring the system parameters and the bias term. Also, we demonstrate that it is possible to control the offset and amplitude of the chaotic signals generated. Compared to some few cases previously reported on systems without linear terms, the plethora of behaviors found in this work represents a unique contribution in comparison with such type of systems. A suitable analog circuit is designed and used to support the theoretical analysis via a series of Pspice simulations.

AN UNUSUAL 3D AUTONOMOUS QUADRATIC CHAOTIC SYSTEM WITH TWO STABLE NODE-FOCI

2010 ◽  
Vol 20 (04) ◽  
pp. 1061-1083 ◽  
Author(s):  
QIGUI YANG ◽  
ZHOUCHAO WEI ◽  
GUANRONG CHEN
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Type Systems ◽  
Homoclinic Orbits ◽  
Stable Node ◽  
Algebraic Form ◽  
Special Cases ◽  
New Chaotic System ◽  
Parameter Values ◽  
New System

This paper reports the finding of an unusual three-dimensional autonomous quadratic Lorenz-like chaotic system which, surprisingly, has two stable node-type of foci as its only equilibria. The new system contains the diffusionless Lorenz system and the Burke–Shaw system, and some others, as special cases. The algebraic form of the new chaotic system is similar to the other Lorenz-type systems, but they are topologically nonequivalent. To further analyze the new system, some dynamical behaviors such as Hopf bifurcation and singularly degenerate heteroclinic and homoclinic orbits, are rigorously proved with simulation verification. Moreover, it is proved that the new system with some specified parameter values has Silnikov-type homoclinic and heteroclinic chaos.

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