Stable predictive control of chaotic systems using selfrecurrent wavelet neural network 45 the layer 4 is an output layer. A search for the simplest chaotic partial differential. Control of chaos, or control of chaotic systems, is the boundary field between control theory and dynamical systems theory studying when and how it is possible to control systems exhibiting irregular, chaotic behavior. Stable predictive control of chaotic systems using self. Implementation of a hyperchaotic system with hidden attractors into. So, the synchronization of chaotic systems can be realized more easily. Over 10 million scientific documents at your fingertips. Unesco eolss sample chapters control systems, robotics, and automation vol. In addition, the output node accepts directly input values from the input layer. Large, successful retailers dont have to worry about lots of small mistakes adding up, and take great care to ensure their systems are always up and running. Thus, chaotic systems like the weather are unpredictable and the flapping of a butterflys wings gives rise to a storm.
Solving hyperchaotic systems using the spectral relaxation. Fradkov encyclopedia of life support systems eolss nonlinear oscillations theory is limit cycle, that is, a periodic trajectory attracting other trajectories starting close to it. Potential function in a continuous dissipative chaotic. 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. Fundamentals of synchronization in chaotic systems. In the encryption process, the keystream is dependent on both the plainimage and the secret key. Naval research laboratory, washington, district of columbia 20375 james f. Chaos theory is a branch of mathematics focusing on the study of chaosstates of dynamical systems whose apparentlyrandom states of disorder and irregularities are often governed by deterministic laws that are highly sensitive to initial conditions. Pdf synchronization in chaotic system researchgate. This paper serves as an introduction to the analysis of chaotic systems, with techniques being developed by working through two famous examples. They are in the frontier between simple and chaotic systems. Of particular interest is the last term of the formula of the main result presented in 7. The stability of adaptive synchronization of chaotic systems francesco sorrentino,1,2 gilad barlev,1 adam b. In this paper, we propose two integrated chaotic systems ics to address the aforementioned limitations of existing 1d and hd chaotic maps.
Chaos theory is an interdisciplinary theory stating that, within the apparent randomness of chaotic complex. Publication date 1992 topics chaotic behavior in systems, differentiable dynamical systems, transport theory. Phase synchronization in regular and chaotic systems 2293 if the rotation number is rational, the observed frequency is in the rational relation with the frequency of the external force. A system can wear order and chaos like different masks, depending on the situation. Pdf a new chaotic system having four paramters is proposed and its dynamics has been studied for different values of the parameters involved. Our preliminary task of establishing the equations, given the physical system, may nevertheless continue to entail some difficulties. A complex system is a system composed of many components which may interact with each other. Play and brain development as complementarynonlinear. It is necessary to design a new chaotic system to overcome the defects referred above. Models of chaotic oscillator networks kostas tsakalis, niranjan chakravarthy and leon iasemidis abstractin an effort to understand basic functional mechanisms that can produce epileptic seizures, and strategies for seizure suppression and control, we discuss some key features. Especially, when designing the controller, we just need to ensure that the diagonal elements of the diagonal matrix are less than or equal 0. This book presents a collection of major developments in chaos systems covering aspects on chaotic behavioral modeling and simulation, control and synchronization of chaos systems, and applications like secure. As said in the section 1, chaotic systems are dynamical systems that defy synchronization, due to their essential feature of displaying high sensitivity to initial conditions.
A third key aspect of chaotic systems is the beautiful order that emerges from them. Chaotic transport in dynamical systems by wiggins, stephen. This result assumes the existence of the probability density function of the input as well as the probability density function of the output. A blockbased image encryption algorithm using wave function and chaotic system is presented. State space chaotic system chaotic dynamic chaotic attractor couette flow.
The rst is the logistic map, a rstorder discrete dynamical system, and the second is the lorenz system, a threedimensional system of di erential. The proposed method, called the multistage spectral relaxation method msrm, is applied for the numerical solution of three hyperchaotic systems. There lies a behavior between rigid regularity and randomness based on pure chance. A new 1d chaotic system for image encryption article pdf available in signal processing 97. Fractional order chaotic systems file exchange matlab. The system modeling problem we assume that we observe the state of a chaotic system through an observation function, h. Chaotic systems for pattern recognition and brain modelling. A new simple chaotic system and its application in medical. Analysis of chaotic time series mathematical theory of chaotic systems identi. An similar expression can be also found in papoulis and pillai 8, pp. Examples of complex systems are earths global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, social and economic organizations like cities, an ecosystem, a living cell, and ultimately the entire universe. The classic chaotic system example is the theoretical butterfly effect, in which the wings of a butterfly cause a variation in the weather hundreds of miles away. A simple deterministic dynamical system may be defined as. Forecasting chaotic systems with very low connectivity.
Pdf a new chaotic dynamical system and its synchronization. Tsim, where h is the time step and yvector of the numerical solution for state. Chaotic dynamics of nonlinear systems internet archive. An excellent chaotic system should aggregate the properties of higher complexity and better chaotic performance. It therefore seems impossible for two chaotic systems to synchronize with each other, but if the two systems exchange information in just the right way. The user may add normal white noise to the systems, change their parameters, or try different initial conditions. Recently, another field, called relativistic chaos, has emerged to describe systems that follow the laws of general relativity. The synchronization of chaotic systems sciencedirect. Potential function in a continuous dissipative chaotic system. Encryption is an effective way to protect these images from security threats. Chaotic systems toolbox file exchange matlab central. One characteristic of a chaotic system is that the signals produced by a chaotic system do not synchronize with any other system. Fundamentals of synchronization in chaotic systems, concepts, and applications louis m.
Differential equations, dynamical systems, and an introduction to chaosmorris w. Disordered systems thierry giamarchi quantum physics. A chaotic system operates according to set rules, but constant feedback, time delays, and tiny changes make the system behave randomly without repetition. Principles and applications of chaotic systems communications of. Quantum chaos theory studies how the correspondence between quantum mechanics and classical mechanics works in the context of chaotic systems. A random sequence generated by the chaotic system is used to find the source point in the wave and produces a diffusion matrix for modular operation. Among the available encryption algorithms, chaosbased methods have strong cryptographic properties, because chaotic systems are sensitive to initial conditions and parameters. We have used onedimensional observations in all of our work to date.
Today, medical imaging suffers from serious issues such as malicious tampering and privacy leakage. Chaos theory is an interdisciplinary theory stating that, within the apparent randomness of chaotic complex systems, there are underlying. By using a constant diagonal matrix, the active control is developed. Another characteristic of chaotic systems is order without periodicity. The stability of adaptive synchronization of chaotic systems. The node output is a linear combination of consequences obtained from the output of the layer 3. This toolbox contains the functions which can be used to simulate some of the wellknown fractional order chaotic systems, such as. Pdf this article introduces a new chaotic system of threedimensional quadratic autonomous ordinary differential equations, which can display i two. A novel adaptive active control projective synchronization. Control of chaos is closely related to nonlinear control, and many methods of nonlinear control are applicable to chaotic systems. Chaotic systems can be very simple, but they produce signals of surprising complexity.
However, the possibility for a computer crash pales in comparison to the numerous, common errors that are spawned by using excel spreadsheets. Constructing potentiallike functions in chaotic systems is an approach already taken by researchers. Isbn 9789533075648, pdf isbn 9789535155089, published 20110214. Chaotic system article about chaotic system by the free.
Semyon dyatlov chaos in dynamical systems jan 26, 2015 3 23. Heagy institutes for defense analysis, science and technology division, alexandria, virginia 223111772. A chaotic encryption scheme for realtime embedded systems. These attempts are successful some times and unsuccessful at others, which is not surprising since most natural and human phenomena have nonlinear dynamic qualities, and play exhibits many characteristics of such systems. A chaotic system can gyrate from order to chaos and back again. Milne so far we have been interested in infinite and clean. The simplest chaotic examples of various types of dynamical systems are instructive because they reveal chaos universal features and basic ingredients, since distilling complicated chaotic systems down to the simplest one reveals the precious few elements essential for chaos. When the system becomes increasingly unstable, an attractor draws the stress and the system splits and returns to. The presentation is a bit quick, and until section 2. 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. Control of chaotic systems encyclopedia of life support.
However, recent work in dynamical systems theory has made clear that the. The more nuances are captured, the more chaotic a system may appear, because those exact same input conditions are not repeated the next time. Differential equations, dynamical systems, and linear algebramorris w. As a result, two identical chaotic systems starting at nearly the same initial points in phase.
141 813 1065 1384 1083 1211 1388 352 333 1599 947 1165 1446 1025 1120 1408 1233 1113 262 210 184 97 1553 461 1364 907 1354 21 901 1091 252 983 430 400 3 438 708 1333 309 1488 973 396 1197 550