In practice, if you didnt have the modulo, it would grow to be a very large positive or negative number the total amount of accumulated phase over time. Chua circuit equations choose as the dynamical variables. Chua circuit are typical models displaying complex behavior. Course registration do the assignments come to the tutorials. Here is the multisim schematic, click for a screen shot. Chaos in the chua circuit nyu tandon school of engineering. One can easily observe that for m0 the system becomes linear. Dimensionless chuas circuit the animation on the left is taken directly from a visualization of a chuas circuit simulation in matlab after running for about 100 seconds and then rotated for viewing. Chaos in the chua circuit project for the course on dynamical systems. The application of numerical methods based on polynomial approximation and multistep algorithm is presented to simulate the behavior of a chaotic oscillator, e.
Simulating chuas circuit return to table of contents first we need to simulate chuas circuit. All your les and all work which you do will be in this folder. An example of an electrical circuit,which is used in this research, is chuas circuit. Michael peter kennedys classic opamp implementation of chuas circuit 2. Chua tbe genesis of chuas circuit following a nontechnical personal reminiscence of the authors conception of chuas circuit, this paper presents the systematic sequence of technical steps which the author used to design his chaotic circuit. The test program computes an impulse response of each resonator, and plots them overlaid. In dynamical systems theory, the bakers map is a chaotic map from the unit square into itself. The following matlab project contains the source code and matlab examples used for chua oscillator. Pdf on oct 10, 2011, trzaska zdzislaw w and others published matlab.
Pdf matlab solutions of chaotic fractional order circuits. Simulink mfile sfunctions o primary purpose simulating nonlinear dynamics with matlab o how they work example mfile sfunction script simulinkusers guidedeveloping sfunctionsoverview of sfunctions explains the basics each iteration, the sfunction performs calculations based on the value of a flag initialize, find. These two papers complement oneanother by collectively providing an adaptive control scheme for every parameter in the chua s oscillator. This program gives the phase portraits of the memristor based chuas circuit. We soon notice that there is a doublescroll attractor, which is a feature of chuas circuit. Chuas circuits are some of the simplest kinds of chaotic circuits. Similar to integerorder differentiation, fractionalorder differentiation fulfils the. Implementation of chuas circuit with a cubic nonlinearity. For example, hidden attractors are attractors in systems without equilibria or with only one stable. The source code and files included in this project are listed in the project files section, please make sure. These beautiful patterns are truly chaotic and can be modeled by relatively. A fast and simple implementation of chuas oscillator using a. Now recover the desktop default layout, so that your matlab window. The relevance of chua s oscillator me personally is that i really like some of the sounds i heard on the youtube clips.
Section 4 concentrates on the famous chuas electronic circuit and section 5. Solving differential equations using simulink uncw. Michael peter kennedy peadar forbes abstract the nonlinearity in chuas oscilla tor is commonly implemented as a threesegment. Finite element dynamic analysis of beams on nonlinear. Chuas circuit is then constructed to generate multiscroll chaotic attractors. Pdf modeling and simulation of a chaotic oscillator by matlab. The following matlab project contains the source code and matlab examples used for memristor based chua oscillator. Chuas circuit diagrams, equations, simlulations and how to build. On the dynamics of a simplified canonical chuas oscillator. Chaos in the chua circuit new york university tandon.
Mar 09, 2015 for the love of physics walter lewin may 16, 2011 duration. Memristor based chua oscillator in matlab download free. These two papers complement oneanother by collectively providing an adaptive control scheme for every parameter in the chuas oscillator. A matlabbased system is presented to model and simulate a chaotic oscillator at the system level of abstraction. For the love of physics walter lewin may 16, 2011 duration. Feel free to click around di erent segments in the matlab window, try resizing or closing some of them. Pdf numerical simulation of chuas circuit oriented to. Choose a web site to get translated content where available and see local events and offers.
Michael peter kennedy peadar forbes abstract the nonlinearity in chua s oscilla tor is commonly implemented as a threesegment. Chua s oscillator, adaptive synchronization, parameter matching, in. Chuas circuit is selected to describe the chaos phenomenon. Modeling and simulation of a chaotic oscillator by matlab. If this license fails to meet the governments needs or is inconsistent in any respect with federal procurement law, the government agrees to return the program and documentation, unused, to the mathworks, inc. An example of an electrical circuit,which is used in this research, is chua s circuit. They are considered to be a classic example of true chaos due to their design and output. Chua s circuit also known as a chua circuit is a simple electronic circuit that exhibits classic chaotic behavior. The theory of chua s circuit chaotic dynamics can be described in many different differential equations. This program gives the phase portraits of the memristor based chua s circuit.
Pdf implementation of chaotic oscillator using matlab. Chaos with matlab carlo f barenghi february 24, 2012 contents i matlab 3 1 matlab basics 3. Applying f ma in the xdirection, we get the following differential equation for the location xt of the center. A fast and simple implementation of chuas oscillator. A fast and simple implementation of chuas oscillator using a cubiclike chua diode keith odonoghue. Chua s oscillator is a system described by a set of three differential equations that can be realized either in digital form or in analog form using opamps and passive circuit components, simple in appearance, but extraordinarily complex in its analysis and behavior. The relevance of chua s oscillator to computer music was explored in some papers and demonstrations in the 1990s. Now recover the desktop default layout, so that your matlab window contains the main features shown in figure 1 again. Practical implementation of chua s circuit with a cubic nonlinearity since the desired l i characteristic of the nonlinear resistor lv in chuas circuit is an oddsymmetric function with respect to origin, here we use the cubic polynomial 7 with the coefficients a0 0,a 0 for the nonlinearity of chuas. Generating multiscroll chuas attractors via simplified. In this paper, by taking an example of lorenz system. Non linear oscillator systems and solving techniques vaibhav bajaj, nihit prakash bitspilani, k. Parameter matching using adaptive synchronization of two. This really gives you a good look at the double scroll attractor from all angles and makes the 3dimensional nature of the output more visceral.
Ok, now its the time to play around a bit with matlab. Chua, who was a visitor at waseda university in japan at that time. In 2008, chua and itoh 4 first constructed memristor oscillators from chua s oscillators by replacing chua s diodes with memristors, where the piecewise linear pwl memristor model was used. Let us consider the chua s equation with a cubic nonlinearity see pivka et al.
We soon notice that there is a doublescroll attractor, which is a feature of chua s circuit. The chua s equation is a model of one of the simplest electronic circuits, exhibiting a wide range of complex dynamical behaviors. Reading complexity in chuas oscillator through music 255 the genetic equipment. The source code and files included in this project are listed in the project files section, please make sure whether the listed source code meet your. It is a very simple circuit that consists of two resistors, two capacitors, one inductance and one diode. As an example, we will use simulink to solve the first order. To start up matlab, go to a university computer cluster and login to your account. Using an oscilloscope you can witness a chuas circuit create the strange attractor known as the double scroll.
I am currently working on a bifurcation diagram for chua s circuit but i am having trouble coming up with code for a bifurcation of a system of equations. I have added two slightly different implementations of chuas oscillator to the list of csound opcodes. A list of matlab functions created for simulation of fractionalorder chaotic systems. The main aim of this tutorial is to translate chua s oscillator model into music, in order to discover and interpret complexity through unexpected media. This innocent looking circuit received a great deal of attention in the 90s in the study of complex nonlinear dynamical phenomena, and has been a leading example. In a general case, this nonlinear oscillator comprises a nonlinear. Chua oscillator in matlab download free open source matlab. One implementation, chuap, uses a piecewise nonlinearity. Submit and come to any tutorial you like but be prepared to change.
In 2008, chua and itoh 4 first constructed memristor oscillators from chuas oscillators by replacing chuas diodes with memristors, where the piecewise linear pwl memristor model was used. Chua s circuit is selected to describe the chaos phenomenon. Simulation of a cubiclike chuas oscillator with variable. Chua circuit equations california institute of technology. The other implementation, cuac, uses a cubic polyonimial nonlinearity. Chuas oscillator is a system described by a set of three differential equations that can be realized either in digital form or in analog form using opamps and passive circuit components, simple in appearance, but extraordinarily complex in its analysis and behavior. Chuas circuit also known as a chua circuit is a simple electronic circuit that exhibits classic chaotic behavior. A useful list of links related to chuas circuit and chaos.
This implementation allows one to change the shape of the characteristic function easily and this makes it easier to place the circuit in a given point of the. Consider a springmass system shown in the figure below. This is a simulation of the chuas attractor solved using rk 4 in matlab. Simulating chua s circuit return to table of contents first we need to simulate chua s circuit. An implementation of a cubiclike chuas oscillator based on a nonlinear resistor implemented with two cmos inverters and two linear resistors is proposed. Dimensionless chua s circuit the animation on the left is taken directly from a visualization of a chua s circuit simulation in matlab after running for about 100 seconds and then rotated for viewing. The genesis of chuas circuit university of california. It is named after a kneading operation that bakers apply to dough. From the start button, select all programs, scientific software and matlab2010b. Chuas circuit is an example of simple electronic circuit with a chaotic behavior. The piecewiselinear nature of the element means that the. Matlab is an acronym for matrix laboratory and is a. A useful list of links related to chua s circuit and chaos.
Chua oscillator function circuit % data for chua s oscillator. The user is advised to try different values for m and see the changes in the system. Spencer and brigham young university this is a tutorial to help you get started in matlab. Parameter matching using adaptive synchronization of two chua s oscillators. Spencer department of physics and astronomy brigham young university c 2000 ross l. An analog chaotic generator chuas oscillator was used in. I am currently working on a bifurcation diagram for chuas circuit but i am having trouble coming up with code for a bifurcation of a system of equations. The theory of chuas circuit chaotic dynamics can be described in many different differential equations. Finite element dynamic analysis of beams on nonlinear foundations under a moving oscillator cristiano vieira rodrigues cristiano. One is on a breadboard, the second is soldered on a gridstyle circuit board, and the third is built on a custom designed pcb and has an extra jack to switch between signals for comparison.
This means roughly that it is a nonperiodic oscillator. Chua s circuits are some of the simplest kinds of chaotic circuits. Figure 18a shows the measured inductor current in standard mode. Dynamicalsystemswithapplicationsusingmatlabindex of. Chua tbe genesis of chua s circuit following a nontechnical personal reminiscence of the author s conception of chua s circuit, this paper presents the systematic sequence of technical steps which the author used to design his chaotic circuit.
In this program you want to see the period doubling scenario please change the control parameter value of r. The electrical circuit depicted in figure 1 is known as the chua circuit. A simplified hyperchaotic canonical chuas oscillator referred as shcco hereafter made of only seven terms and one nonlinear function of type hyperbolic sine is analyzed. Non linear oscillator systems and solving techniques. A matlab based system is presented to model and simulate a chaotic oscillator at the system level of abstraction. Using an oscilloscope you can witness a chua s circuit create the strange attractor known as the double scroll. In this paper the synchronization of two chua circuits is simulated. For illustration is presented an example of using the matlab function created for the fractionalorder. This section provides matlaboctave program listings for the sinusoidal resonatoroscillator algorithms discussed above. You can get the value from the reference which is quoted in this program. Based on your location, we recommend that you select. Michael peter kennedy peadar forbes abstract the nonlinearity in chuas oscillator is commonly implemented as a threesegment piecewiselinear resistor.
Update the question so it s ontopic for mathematica stack exchange. Chuas oscillator is the first analog electronic circuit that was proved to exhibit chaotic behavior such as bifurcation, chaotic attractors, and so on. Birla goa campus, india abstract the paper involves thorough study of nonlinear vibratory oscillators and numerical methodology to analyse and resolute the nonlinear dynamical world. Java project tutorial make login and register form step by step using netbeans and mysql database duration. A fast and simple implementation of chua s oscillator using a cubiclike chua diode keith odonoghue. Initially you can vary the resistance value r to see the period doubling scenario. Chuas circuit diagrams, equations, simlulations and how. Matlab tutorial eth zurich, department of biosystems science and engineering dbsse. Chua oscillator in matlab download free open source. In figure a you can see three versions of chuas circuit. Pdf matlab programming for engineers stephen lynch fima. This circuit will be used in the experimentsof controlling chaos.
Electronics free fulltext active emi reduction using. You can go through the videos either before or after completing this tutorial. Feb 21, 20 java project tutorial make login and register form step by step using netbeans and mysql database duration. Synchronization of coupled oscillators in matlab youtube. Sep 30, 2015 this is a simulation of the chua s attractor solved using rk 4 in matlab. Michael peter kennedy s classic opamp implementation of chua s circuit 2.
1473 669 805 494 254 579 1537 1312 737 278 1362 1606 407 1335 1375 929 1552 720 1113 1238 1186 500 1477 752 175 1535 1351 909 601 711 1594 978 1394 303 111 1009 538 421 447