Continuous Chaotic System Research Articles

Hyper-chaotic LÜ System Simulation Design of Digital Circuit Based on DSP Builder

In order to overcome sensitive defects of components deviations and environment defects in analog circuit design, a novel four-dimensional hyperchaotic systems is constructed based on LU system. Basic nonlinear dynamics characteristics are analyzed to the new system. By optimizing the design of sampling frequency selection, gain adjustments, parameter configuration etc., the hyperchaotic circuit runs stably while the signal amplitude is reasonably controlled. Curves of the digital chaotic sequence show smooth without jagged shape. The circuit can be applied to other digital realization of chaotic systems with commonality and expandability. Its experimental results fully consistent with phase space structures of the continuous chaotic system, which shows the development of chaotic systems based on FPGA is feasible and practical. DOI: http://dx.doi.org/10.11591/telkomnika.v11i5.2503 Full Text: PDF

Analysis on stability of continuous chaotic systems

The notion of k-error exhaustive entropy was proposed,based on exhaustive entropy.It was used to measure the strength of random-like property of chaotic sequences,and its two basic properties were proved.Then the method was used to analyze the stability of random-like property of three common continuous chaotic systems,such as Lorenz system,Rssler system,and Chua's system.The simulation results show that the approach can reflect the random essence of continuous chaotic system and Chua's system is better than Lorenz system and Rssler system as the source of randomness.

Synchronized hybrid chaotic generators: Application to real-time wireless speech encryption

In this paper, a new stream key generator Hybrid Discrete Continuous Chaotic System (HDCCS) based on continuous and discrete chaotic systems is proposed. Our solution provides an easy and robust chaos synchronization while decrease the degradation due to finite precision during a digital implementation. Real-time application to wireless speech encryption effectively hides the original signal. Statistical security analysis for the proposed cryptosystem against cryptanalysis attacks, from a strict cryptographic viewpoint, are presented. These results verify and prove that the proposed speech cryptosystem is highly secure and has a very powerful diffusion and confusion mechanisms widely used in conventional cryptography.

A new 3D chaotic system with golden proportion equilibria: Analysis and electronic circuit realization

This article introduces a new three-dimensional quadratic continuous autonomous chaotic system with golden proportion equilibria, which can generate single folded attractor. Some basic dynamical behaviors and the dynamical structure of the new chaotic system are investigated either analytically or numerically. Finally, the chaos generator of the new chaotic system was designed, simulated and experimentally confirmed via a novel electronic circuit design. A good qualitative agreement is illustrated between the simulations and the experimental results. It is convenient to use the new system to purposefully generate chaos in chaos applications. The new system has eight terms, two quadratic nonlinearities and two parameters (a and b). The new chaotic attractor equations have three equilibrium points and more interestingly the equilibrium points have golden proportion values.

A third-order sliding-mode observer for a continuous delay chaotic system

This paper aims firstly to highlight the possibility of recovering a message included in a chaotic continuous time delay system, secondly to show that it is possible to use the third order sliding mode in order to recover directly all the states and the unknown input (message), thirdly to illustrate the robustness of the proposed observer with respect to a noisy signal. This work is based on the concept of left invertibility and recent advances in sliding mode observers. Some theoretical recalls and assumptions are done previously to the presentation of the observer design and the simulation results.

A Novel Impulsive Control Synchronization of a Lorenz Chaotic Scheme with Special Parameters

One of the common problems of chaos-based secure communication is all these methods need control signal be transmitted in public channel between connectors. Attacker can reconstruct the chaotic system or estimate parameters by using the information of the chaotic system which can be obtained by analyzing the control signal. Therefore we propose a hybrid chaotic synchronization control scheme which contains both continuous chaotic system with Special oscillating parameters and discrete chaotic system. The two systems can get synchronized without control signal transmitting which has reduced the risk of the security.

The Stability of Hybrid Liu Chaotic System with a Sort of Oscillating Parameters under Impulsive Control

The control of chaotic synchronization have to transmitting control signal which increase the security risks of the communication system. Attacker can reconstruct the chaotic system by using the information of the chaotic system. In this paper we propose a hybrid Liu chaotic synchronization control scheme which contains both continuous chaotic system with a sort of oscillating parameters and discrete chaotic system. By theory of impulsive differential equations, we proved a theorem that two continuous Liu chaotic systems can get synchronized without control signal transmitting which has reduced the risk of the security.

Analysis, nonlinear control, and chaos generator circuit of another strange chaotic system

In this paper, we introduce a new 3-dimensional quadratic continuous autonomous chaotic system. This system can generate strange and interesting attractors. Some basic dynamical properties, such as bifurcations, and chaotic behaviors of the new chaotic system are investigated analytically and numerically. We propose a nonlinear control scheme to discuss codimension 1 and 2 Hopf bifurcations. In addition, a new circuit implementation of the chaotic attractor is reported and examined in PSpice. The new system is suitable for purposefully generating chaos in chaos-based engineering applications.

The Synchronization of Super-Chen Chaotic Scheme with a Sort of Oscillating Parameters

Most properties of Super Chen’s chaotic system satisfy with the requirements of secure communication and cryptography. Implusive stabilzation for control and synchronization of Super Chen’s chaotic systems can be applied in secure communication. Super Chen’s Chaotic synchronization control can be the kernel technology in chaos-based secure commu-nication. In this paper we propose a hybrid Super Chen chaotic synchronization scheme control which contains both continuous chaotic system with a sort of oscillating parameters and discrete chaotic system. If oscillating parameters approach to 0, we proved that two systems can get synchronized without control signal transmitting.

The Model of Super-Chen Chaotic Scheme with Oscillating Parameters under the Impulsive Control

The control of chaotic synchronization is the kernel technology in chaos-based secure communication. Those control methods have to transmitting control signal which increase the security risks of the communication system. Attacker can reconstruct the chaotic system or estimate parameters by using the information of the chaotic system. In this paper we propose a hybrid Super Chen chaotic synchronization scheme control which contains both continuous chaotic system with oscillating parameters and discrete chaotic system. If oscillating parameters satisfyingwhen , we proved that two systems can get synchronized without control signal transmitting.

The Model of Liu Chaotic Synchronization with Oscillating Parameters under the Impulsive Control

The control of chaotic synchronization is the kernel technology in chaos-based secure communication. Those control methods have to transmitting control signal which increase the security risks of the communication system. Attacker can reconstruct the chaotic system or estimate parameters by using the information of the chaotic system. In this paper we propose a hybrid Liu chaotic synchronization control scheme which contains both continuous chaotic system with oscillating parameters approach to 0 and discrete chaotic system. By theory of impulsive differential equations, we proved a theorem that two continuous Liu chaotic systems can get synchronized without control signal transmitting which has reduced the risk of the security.

A New Chaotic Behavior from Lorenz and Rossler Systems and Its Electronic Circuit Implementation

This paper presents a new three-dimensional continuous autonomous chaotic system with ten terms and three quadratic nonlinearities. The new system contains five variational parameters and exhibits Lorenz and Rossler like attractors in numerical simulations. The basic dynamical properties of the new system are analyzed by means of equilibrium points, eigenvalue structures. Some of the basic dynamic behavior of the system is explored further investigation in the Lyapunov Exponent. The new system examined in Matlab-Simulink and Orcad-PSpice. An electronic circuit realization of the proposed system is presented using analog electronic elements such as capacitors, resistors, operational amplifiers and multipliers.

Chaotic Cipher Using the Duffing Equation

ABSTRACT We propose a plain files cipher by means of a stream cryptosystem scheme with chaotic addition and a symmetric key. The sequence of numbers used for encryption is generated by a continuous chaotic dynamical system; in particular, we choose the forced Duffing equation since this kind of systems is sensitive to the initial conditions. In a chaotic system, the answer can became periodic during the process of numeric integration. We introduce an heuristic method to break this periodicity.

Impulsive homoclinic chaos in Van der Pol Jerk system

A 3D continuous autonomous chaotic system is reported, which contains a cubic term and six system parameters. Basic dynamic properties of the new Van der Pol Jerk system are studied by means of theoretical analysis and numerical simulation. Based on the Silnikov theorem, the chaotic characterisitics of the dynamic system are discussed. Using Cardano formula and series solution of differential equation, eigenvalue problem and the existence of homoclinic orbit are studied. Furthermore, a rigorous proof for the existence of Silnikov-sense Smale horseshoes chaos is presented and some conditions which lead to the chaos are obtained. The formation mechanism indicates that this chaotic system has impulsive homoclinic chaos, and numerical simulation demonstrates that there is a route to chaos.

Wireless chaotic speech communication via digital signal processor ——system design and hardware implementation

提出了一种基于数字信号处理器（DSP）的语音无线混沌数字通信系统设计与硬件实现的新方案. 根据Runge-Kutta算法和变量比例扩张变换，以多涡卷广义Jerk系统为例，对其连续混沌系统作离散化处理，产生作为语音数据加密与解密的混沌数字序列. 在芯片型号TMS320VC5509APGE的DSP技术平台上，利用无线发送器和无线接收器nRF2401，实现了语音无线混沌数字通信. 给出了技术设计与硬件实现结果，证实了该方案的可行性.

A new chaotic attractor from general Lorenz system family and its electronic experimental implementation

This article introduces a novel three-dimensional continuous autonomous chaotic system with six terms and two quadratic nonlinearities. The new system contains two variational parameters and exhibits Lorenz-like attractors in numerical simulations and experimental measurements. The basic dynamical properties of the new system are analyzed by means of equilibrium points, eigenvalue structures, and Lyapunov exponents. The new system examined in Matlab-Simulink^{\textregistered} and Orcad-PSpice^{\textregistered}. An electronic circuit realization of the proposed system is presented using analog electronic elements such as capacitors, resistors, operational amplifiers and multipliers. The behaviour of the realized system is evaluated with computer simulations.

Theoretic and Numerical Study of a New Chaotic System

This paper introduced a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different from the Lorenz system and other existing systems. Basic properties of the new system are analyzed by means of Lyapunov exponent spectrum, Poincaré mapping, fractal dimension, power spectrum and chaotic behaviors. Furthermore, the forming mechanism of its compound structure obtained by merging together two simple attractors after performing one mirror operation has been investigated by detailed nu-merical as well as theoretical analysis. Analysis results show that this system has complex dynamics with some interesting characteristics.

Existence of a new three-dimensional chaotic attractor

In this paper, one heteroclinic orbit of a new three-dimensional continuous autonomous chaotic system, whose chaotic attractor belongs to the conjugate Lü attractor, is found. The series expression of the heteroclinic orbit of Šhil’nikov type is derived by using the undetermined coefficient method. The uniform convergence of the precise series expansions of this heteroclinic orbits is proved. According to the Šhil’nikov theorem, this system clearly has Smale horseshoes and the horseshoe chaos.

Chaotic digital communication system based on field programmable gate array technology—Design and implementation

A novel universal approach for design and implementation of chaotic digital communication system based on IEEE-754 standard and field programmable gate array technology (FPGA) is proposed, combing chaos encryption with traditional cipher realization. By using the Euler algorithm and appropriate discrete processing, the continuous chaotic system is converted to a discrete chaotic system. Using FPGA hardware design system, digital chaotic sequence is generated as the key. Scrambling and expansion encryption algorithm is realized and analyzed. Driven and response of secure communication system is designed by constructing a loop including the signal and achieving chaotic synchronization between sender and receiver. Taking grid Chua chaotic system as an example, the secure communication system using FPGA hardware platform is implemented. The technical development process, algorithm flow chart, hardware design and realization result are also given.

A chaos-based CDMA scheme with a chaos-based encryption algorithm

An encryption algorithm based on a discretized chaotic map controlled by a Δ-modulated feedback is applied to a direct sequence code-division-multiple-access (DS-CDMA) scheme, which improves security at the cost of lowering the performance of bit error rate (BER). However, numerical simulations show that the DS-CDMA scheme still has a satisfactory performance by means of the spreading sequences generated by a continuous chaotic system. These spreading sequences are chosen from the local maximums of the output of the continuous chaotic system. This scheme is also robust against the channel noise.