Naval research laboratory, washington, district of columbia 20375 james f. Moreover, the synchronized systems are implemented in two tms320f28335 dsp boards which are connected by a serial port and the output signals are exhibited by. Design of a 12term hyperchaotic system with four quadratic nonlinearities and its labview implementation. But in sometimes, chaos effect is undesirable in practice, and it restricts the operating range of many electronic and mechanical devices 15. Differential equations, dynamical systems, and linear algebramorris w. A novel 5ddimentional hyperchaotic system and its circuit. Research article control and synchronization of chaotic and. Solution and dynamics analysis of a fractionalorder. Differential equations, dynamical systems, and an introduction to chaosmorris w.
Systems is allowed to offer this version of the iso standard as a free pdf file on its web site. In recent years, notable contributions have been made to generation of hyperchaotic systems 7, 8, 9. Chaotic systems are dynamical systems that are highly sensitive to initial conditions. As we know, chaos is an important topic in nonlinear science 5, 8. Dynamic analysis of a 5d fractionalorder hyperchaotic system. Weuseanrcconstructknownasanechostatenetwork,8which uses a network of nodes as the internal reservoir. For this 5d hyperchaotic system, the stability of equilibrium points is analyzed by means of the stability theory of fractional systems. Different ways to access pdf files with firefox firefox help. In addition, the output node accepts directly input values from the input layer. Mar 27, 2017 in this paper, the fractionalorder 5d hyperchaotic system is proposed based on the hyperchaotic lorenz system. The henon map the ikeda map the logistic map the quadratic map the lorentz flow the mackeyglass flow the rossler flow. A sixdimensional hyperchaotic system selection and its. First, we assume that there is a common factor in gxt of.
New family of 4d hyperchaotic and chaotic systems with. Adaptive fuzzy synchronization of fractionalorder chaotic. Download chaotic systems pdf ebookchaotic systems chaotic systems ebook author by james lawrence chaotic systems ebook. Njah 2 nonlinear dynamics research group, department of physics, federal university of agriculture, pmb, abeokuta, nigeria. Next, according to various forms of the nonlinear part gxt, the following ts fuzzy modeling method for hyperchaotic systems is given below. Synchronization, control and stability of fractional order. Fradkov institute for problems of mechanical engineering, russian academy of sciences, st. L e c t u r e 1 w h a t i s c h a o s university of arizona. Numerical simulation of the synchronized systems is carried out, and it is found that the synchronization phenomenon can be observed in both state variables and intermediate variables. Design of a 12term hyperchaotic system with four quadratic. Chaoticsystemsdynamics,algorithmsandld694892020 adobe acrobat reader dcdownload adobe acrobat reader dc ebook pdf.
The ts fuzzy model with its small number of fuzzy ifthen rules is employed to represent many typical nonlinear hyperchaotic systems. Encyclopedia of life support systems eolss analysis of chaotic systems a. Digital chaotics creates visual music videos using 3d animation and highly sophisticated software. Chaos, nonlinear systems, nonlinear dynamics, chaotic behavior, attractor. According to the boundedness of hyperchaotic systems, one can assume that xit 2 c. Combination synchronization of fractional order nchaotic systems. Learn how to change how pdfs are viewed in firefox with either the builtin viewer or a third party tool. Fundamentals of synchronization in chaotic systems. Links below point to my pdf files for the five projects i completed. They can be signed electronically, and you can easily view pdf files on. Heagy institutes for defense analysis, science and technology division, alexandria, virginia 223111772.
The user may add normal white noise to the systems, change their parameters, or try different initial conditions. Play and brain development as complementarynonlinear dynamic chaoticcomplex systems dr. The optimal c chosen by minimizing e c is to guarantee that the n thorder solution 8. An adaptive controller, accompanied with fractional adaptation law, is established, fuzzy logic systems are used to approximate the unknown nonlinear functions, and the fractional lyapunov stability theorem is used to analyze.
Hyperchaotic system, which has at least two positive lyapunov exponents, has more complex dynamic behaviors and can be more useful in many applications such as chaotic communication systems. There exist some wellknown hyperchaotic systems such as hyperchaotic rossler system 2, hyperchaotic chen system 2 and so on 3,4,5,6,7,8. Additional functions provided for phase space reconstruction, surrogate data simulation of the linear characteristics of a time series, dimension and noise estimation, and noise reduction. Disconnectedchaotic attractors in digitally controlled linear. Oct 21, 2011 indeed, since continuous hyperchaotic systems are necessarily fourdimensional, the effect of the measurement function \h. Fundamentals of synchronization in chaotic systems, concepts, and applications louis m.
Chaotic control and generalized synchronization for a. The main idea is to use a block diagonal matrix in the design of the nominal system, so as to construct a desired hyperchaotic system. Solving hyperchaotic systems using the spectral relaxation method. Chaotic and nonchaotic behavior in threedimensional. I learned a lot and learned that i need to learn a lot more.
Antisynchronization of the hyperchaotic liu and hyperchaotic. The sensitive nature of chaotic systems is commonly called as the butterfly effect 1. Chaos on the lorenz attractor 14 acknowledgements 17 references 17. For this realistic property, fractional calculus which was in earlier stage considered as mathematical curiosity now becomes the object of.
Milne so far we have been interested in infinite and clean. Stable predictive control of chaotic systems using selfrecurrent wavelet neural network 45 the layer 4 is an output layer. Download free acrobat reader dc software, the only pdf viewer that lets you read, search, print, and interact with virtually any type of pdf file. Chaotic map based dsss file exchange matlab central. Each of the systems in this paper is rescaled as in the following example. Control of chaos is closely related to nonlinear control, and many methods of nonlinear control are applicable to chaotic systems. Issn 17493889 print, 17493897 online international journal of nonlinear science vol. Theres a widevariety of free pdf readers available for every operating system and platform. Research article control and synchronization of chaotic and hyperchaotic lorenz systems via extended backstepping techniques o. Chaos theory has been applied to a variety of fields like physical systems 3, chemical systems 4, ecological systems 5, secure. Adobe reader and acrobat will enforce the fileopen. Thats why we invented the portable document format pdf, to present and exchange documents reliably independent of software, hardware, or operating system. Forecasting chaotic systems with very low connectivity. This paper aims at developing a unified chaotification framework for generating desired higherdimensional dissipative hyperchaotic systems by using a singleparameter controller.
Many scholars have studied the synchronization control problems for fractionalorder chaotic systems. Play and brain development as complementarynonlinear. School of electronics and information engineering, harbin institute of technology, harbin, china. Living systems typically have many interrelated parts, and the output, or behavior. The role of convergence acceleration parameter is to rearrange the expansion of series solution 7. This toolbox contains a set of functions which can be used to simulate some of the most known chaotic systems, such as. Theoutputofeach nodeinthenetworkisfedintotheoutputlayeroftherc,whichper forms a linear operation of the node values to produce the output of the rc as a whole.
In coming days i will be updating it with complete chaos based generators frequency hopping and cdma systems with multiple users and till the underwater acoustic networks phase. Chaoticsystemsdynamics,algorithmsandld694892020 adobe. A first course in chaotic dynamical systems solutions. Every node has inputs, drawn from other nodes in the reservoir or from the input to the rc, and every input has an associated weight. This open source program runs on all major operating systems, allowing you to merge pdf files, interactive forms, bookmarks, and more. A sixdimensional hyperchaotic system selection and its application in dscdma system. The henon map is defined by two equations and depends on two parameters a and b, and the system exhibits a strange attractor for a 1.
Karthikeyan professor, department of electronics engineering, defence engineering college, debrezeit, ethiopia. Stable predictive control of chaotic systems using self. Using switching systems, some new chaotic attractorshavebeenachieved inliu et al. Also, the methods to generate chaos are more and more diversi. A new hyperchaotic system and its generalized synchronization. Synchronization of fractionalorder chaotic systems with. A new multistage numerical method based on blending a gausssiedel relaxation method and chebyshev pseudospectral method, for solving complex dynamical systems exhibiting hyperchaotic behavior, is presented. Table 2 describes the systems dynamics, location of equilibria, shape of equilibria, lyapunov exponents, nature of the systems, lyapunov dimensionkaplanyorke dimension d ky and initial conditions used for simulation of these cases. A static output feedback fuzzy soff control approach is proposed in order to deal with the problem of synchronization of two identical hyperchaotic systems. Synchronization of fractionalorder chaotic systems with gaussian fluctuation by sliding mode control yong xu, hua wang department of applied mathematics northwestern polytechnical university, xian, 710072, china abstract this paper is devoted to the problem of synchronization between fractionalorder.
Analysis and projective synchronization of new 4d hyperchaotic system in this manuscript, a new 4d hyperchaotic system is designed which is based on the 3d chaotic system 32 by introducing one more state variable in order to get the new 4d system. Learn more about digital image processing, code generation, chaotic sequence image processing toolbox. Disordered systems thierry giamarchi quantum physics in. This program deals with spread spectrum communication systems using chaos as the sequence generators. Rm \mapsto r\ becomes more critical than for threedimensional continuous chaotic systems for its possibly introducing spurious foldings since the projection of an object in \rm\ unto \r\ will most likely result.
Thus, the equation of motion of the uncontrolled system assumes the following form. Let the chaotic fractional system of lorentz take place 7. Ilmi approach to static output feedback fuzzy control for. Constructing hyperchaotic systems at will shen 2015. The worlds best pdf solution lets you create sign and send documents on any device view and annotate pdf files with acrobat reader dc you can do. A nonautonomous technique to generate multiscroll attractors and hyperchaos has been introduced 1719. Further investigations of nonlinear systems, both theore. We investigate the synchronization problem of fractionalorder chaotic systems with input saturation and unknown external disturbance by means of adaptive fuzzy control. Chaos control and synchronization of a novel 5d hyperchaotic. Empower your teams to do their best work with unlimited esigning and the ability to create, convert, combine, edit, sign, and share pdfs. Control and synchronization of a new hyperchaotic system with.
Fractionalorder chaotic systems are often three or fourdimensional. So, in 9 was noted that dimension of such systems can be defined by the sum of fractional exponents 3, and is the most effective. The shapes of equilibria of the eight cases from the three proposed systems are shown in fig. Since the pioneering work of pecora and carroll 2, chaos synchronization has been studied extensively and intensively in the last two decades 217. Aug 15, 2014 chaotic sequence generation from chens. The henon map is one of the discrete dynamical systems that exhibit chaotic behaviors. These traits are favorable to information security and have attracted the attention of cryptographers to develop.
Since the seminal work of pecora and carroll 2, chaos synchronization has been studied extensively in the last two decades 217. The portable document format pdf is a format intended for exchange documents it was developed by adobe systems the creation of pdf files is very easy with the free pdf24 creator find out how you can create pdf files which is as easy as printing. Thisresultbecamethe first rigorous confirmation of chaotic properties exhibited by dynamical systems not involving any random mechanism. How to merge pdf files without acrobat 247 shutterstock. Chaotic systems toolbox file exchange matlab central. Afirstcourseinchaoticdynamicalsystemssolutions 23 pdf drive search and download pdf files for free. Some typical multiscroll attractors and hyperchaotic systems are presented in 917. I am simultaneously a choreographer, a cinematographer, a colorist, a software designer, a user experience designer, an entrepreneur, a scientist, a mathematician, an audience member, and a critic of myself, and othe. Control of chaotic systems encyclopedia of life support systems. So far, there are many control methods for fractionalorder.