Metinvaran Paper

CHAOTIC WEB SIMULATION LABORATORY APPLICATION Metin VARAN1 ,Yılmaz UYAROĞLU2 Zekeriya ÖZDEMİR3 Fahri VATANSEVER4 Mehmet Ali YALÇIN5 1

PhD Student Electrical Engineer Faculty Member Sakarya University Electrical-Electronics Engineering Dept. Asst. Prof ,Sakarya University Electrical-Electronics Engineering DepT. 3 M.Sc.Electrical Engineer Faculty Member of Sakarya University Electrical-Electronics Engineering Dept 4 Asst. Prof ,Sakarya University Technical Education Dept 5 Prof ,Sakarya University Dean of Engineering Faculty 1 e-mail: [email protected] 2e-mail: [email protected] 3 e-mail: [email protected] 4 e-mail: [email protected] 5e-mail: [email protected] 2

Abstract - Chaotic applications recently have been used for various different fields and studies. In this study, we target to model and analyze fundamental chaotic oscillators by using web tools. Among many oscillators, we have focused on Lorenz Oscillators both modeling and analyzing. With this study we aim to satisfy calculation capability of basic chaotic models using web Medias and make chaotic models more observable and understandable. Keywords - Chaotic Simulation Laboratory Application, Digital Media, MATLAB Calculation Engine, Chaotic Methods 1.INTRODUCTION We review recent developments in the modeling and prediction of nonlinear time series. In some cases, apparent randomness in time series may be due to chaotic behavior of a nonlinear but deterministic system. In such cases, it is possible to exploit the determinism to make short term forecasts that are much more accurate than one could make from a linear stochastic model. This is done by first reconstructing a state space, and then using nonlinear function approximation methods to create a dynamical model. Nonlinear models are valuable not only as short term forecasters, but also as diagnostic tools for identifying and quantifying low-dimensional chaotic behavior. During the past few years, methods for nonlinear modeling have developed rapidly, and have already led to several applications where nonlinear models motivated by chaotic dynamics provide superior predictions to linear models. These applications include prediction of fluid flows, sunspots, mechanical vibrations, ice ages, measles epidemics, and human speech.[1]

2.PURPOSE OF STUDY

Web-based educational simulation is not a new area, however due to the difficulties that exist in its utilization, the complexity and specificities of nonlinear dynamic system applications, lecturers have been forcing open in a massive way to the explain and analyze of chaotic modeling in the different engineering problems. This led us to develop the chaotic simulation model that gives a collection of requirements, orientations and prescriptions to the author so that Web-based simulation is used in a proper way in an educational environment. [2,3] The main objective of the study is to simulate and analyze chaotic modeling on the web interface. Deeper goals: building internet-based education tools and intranet objects for chaotic model interesteds and students, which might be separate configurable and separate compiled, for stand alone running; linking configured objects for complex simulation and animation with zoom and mouse-over facilities; ability of strength calculation engine-MATLAB, web publishing of the simulators; building tools for user scenario; report- generator. With this study we aim to satisfy calculation capability of basic chaotic models using web Medias and make chaotic models more observable and understandable. 3.CHAOTIC OSCILLATORS There are many chaotic oscillators used for chaotic modeling and analyzing, generally each oscillator is applied for specific areas. Most fundamental oscillators may be listed as follows: Lorenz, Chua, Rossler, Vanderpol and Duffing Chaotic Oscillator.[4].Lorenz Oscillator is applied for atmospheric studies; Chua Oscillator are applied for electronic circuits, Rossler Oscillators are applied for chemical phenomenon. 4. THE LORENZ ATTRACTOR: A NONLINEAR SYSTEM WITH KNOWN DYNAMICS

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The Lorenz system is a model of convection (i.e., heat transfer) in the atmosphere. The dynamics (i.e., changes in states) of the Lorenz model can be characterized with three first order differential equations,

 .   x1   ( x  x ) 2 1     .    x   rx1  x 2  x1 x3  2   .      bx 3  x1 x 2  x3    

        

(1)

Where X, Y, and Z correspond to the three dynamical variables (corresponding to two temperature measures and a velocity measure), the over-dot corresponds to the rate of change (i.e., derivative) of the variable in question, and a, b, and c are constant parameters. What makes the Lorenz system a complex, nonlinear system is the interaction of the three dynamical variables. As can be seen in Equations above, changes in X are dependent not only upon the value of X, but also upon the values of Y and Z. Therefore, the influences of the variables X, Y, and Z on the current state of the system are not independent and additive, but are instead mutually dependent and multiplicative. The interactive nature of dimensions along which a system may change embodies the complexity of nonlinear systems and is also the key to quantifying systems with unknown or unmeasured dynamical variables[5].

MATLAB and then deploy them as components in .NET and COM environments. You can use the high-level, matrix-optimized language and test your applications. Once the applications are complete, you can use the builder to automatically package them as components and integrate them in .NET and COM applications. To deploy your component, you first install the MCR on the target machine. The MCR is the full set of shared libraries required for executing MATLAB based components. It provides complete support for all features of the MATLAB language and most related toolboxes.After instantiating an object from a MATLAB based component, you can access the object methods just as you access the methods of any other COM or .NET class. COM and .NET data types passed to MATLAB functions are automatically converted to MATLAB data types. Hie builder also provides data conversion classes for manually converting data and managing output data, as well as an interface that converts MATLAB data types into .NET native data types[6]. 6.CHAOTIC WEB SIMULATION LABORATORY APPLICATION Chaotic Web Simulation Applications Main Page involves simulation of basic chaotic models under given initial conditions (Fig.1). This web application runs at an intranet network server, this server only should have MATLAB core engine, not commercial toolboxes. In this study, we state our Web Simulation Application on our intranet servers .

5.MATLAB .NET BUILDER TOOLBOX MATLAB Builder- NE creates MATLAB* based .NET and COM components for royalty-free deployment on desktop machines or Web servers. As a result, one can integrate his MATLAB applications into organizations .NET and COM programs. The builder creates the components by encrypting MATLAB functions and generating either a .NET or COM wrapper around them. One can reference MATLAB based .NET and COM components as one would any other .NET assembly and COM object, for easy integration with existing applications. The components created by the builder run against the MATLAB Compiler Runtime (MCR), the full set of shared libraries that support MATLAB. The MCR is provided with MATLAB Compiler. To run .NET and COM components, it must be distributed the MCR with them. Components created in MATLAB and the MCR can be deployed royalty-free.

Figure 1. Chaotic Web Simulation Laboratory Main Page The Lorenz attractor could be generated only by numerical approximations on a computer, as shown (Fig. 2-Fig.5). Now we have a rigorous proof that confirms its existence. Figure-2 shows x-y portrait of Lorenz System Attractor

For Web applications, the builder provides AJAX-based zoom, pan, and rotate controls for figures created in MATLAB and an API for automatically converting between .NET or COM data types and MATLAB data types. Together, MATLAB, MATLAB Compiler, and MATLAB Builder NE enable you to develop applications using 2

Figure 2. Lorenz Simulation Web Page-1 The Lorenz System’s x-y-z attractor obtained using state equations by Matlab modeling under initial conditions, a=0.5, x0=0.001, y0=0.001, and z0=0. Figure-3 shows x-z portrait of Lorenz System Attractor

Figure 4. Lorenz Simulation Web Page-3 The geometry of the attractor is closely related to the ‘flow’ of the equations that the curves corresponding to solutions of the differential equations. There is an unstable equilibrium, a saddle point, at the origin. The curves repeatedly pass this point, and are pushed away to the left or right, only to circle round to pass back by the saddle. As they loop back, adjacent curves are pulled apart. This is how the unpredictability is created and can end up on either side of the saddle. The result is an apparently random sequence of loops to the left and right. Figure-5 shows Time series of Lorenz System Attractor

Figure 3. Lorenz Simulation Web Page-2

Figure 5. Lorenz Simulation Web Page-5

Figure-4 shows y-z portrait of Lorenz System Attractor 7. CONCLUSIONS Chaotic Web Simulation Laboratory Application aims that satisfying calculation capability of basic chaotic models using web Medias and make chaotic models more observable and understandable. Finally, it is shown that using ASP. NET and C#.NET tools is a flexible way, especially for benefiting ability 3

of MATLAB engine. Subsequent study proposal might be on a real-time web control and web analysis for a chaotic oscillator circuit. 8.REFERENCES [1] CASDAGLI, M., Eubank, S.; Electric Power Research Institute (EPRI) Workshop on Applications of Chaos, San Francisco, Dec. 1990 [2] YANG,O., YABO D. “A Web-Based Virtual Laboratory System for Electronic Circuit Simulation”,May-2005, [3] NICOL , D., JOHNSON, M., YOSHIMURA,A., A Javabased Distributed Simulation Engine, 1998 International Workshop on Modeling Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS) ,Montreal, Canada, pp. 233-240, 1998 [4] ZHANG,X., Department of Computer Tianjin University of Technology and Education, August-2004, [5] A.C. Fowler, M.J. McGuinness; “A description of the Lorenz attractor at high Prandtl number”, Physica D.,. 5, pp. 149–182 1982 [6]http://www.mathworks.com/products/netbuilder/description2. html

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