simulation@uflorida.cis.ufl.edu (Moderator: Paul Fishwick) (01/24/89)
Volume: 7, Issue: 5, Mon Jan 23 17:15:43 EST 1989 +----------------+ | TODAY'S TOPICS | +----------------+ SPECIAL ISSUE: Dynamical Systems Software and Textbooks * Moderator: Paul Fishwick, Univ. of Florida * Send topical mail to: simulation@uflorida.cis.ufl.edu * Archives available via FTP to bikini.cis.ufl.edu, login as 'anonymous', use your last name as the password, change directory to pub/simdigest. ----------------------------------------------------------------------------- Date: Mon, 23 Jan 89 16:20:27 EST From: Paul Fishwick <fishwick@fish.cis.ufl.edu> To: simulation@ufl.edu [[I THOUGHT READERS MIGHT BE INTERESTED IN THIS INFORMATION ON DYNAMICS SOFTWARE AND TEXTBOOKS summarized by Cliff Joslyn at SUNY Binghamton -PAF]] >From: vu0112@bingvaxu.cc.binghamton.edu (Cliff Joslyn) Newsgroups: comp.theory.dynamic-sys,comp.theory.self-org-sys,sci.math,sci.misc,sci.math.symbolic Subject: Course in Dynamics Systems - Recap Date: 23 Dec 88 05:42:17 GMT Organization: SUNY Binghamton, NY Xref: uflorida comp.theory.dynamic-sys:146 comp.theory.self-org-sys:65 sci.math:3718 sci.misc:2969 sci.math.symbolic:393 Some people may recall last month I posted a request for information and feedback about an independent study program in Dynamic Systems Theory that I was helping to develop here at SUNY-Binghamton. The responses were quite helpful, and I would like to take this opportunity to thank everyone who talked w/me by e-mail and news, tell you where we stand now, and post a summary of responses. In my original posting I asked for references to texts, core works, and software systems. At this point I am aware of the following texts: Guckenheimer and Holmes, _Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields_, Springer-Verlag, 1983 (apparently the most mathematically sophisticated and comprehensive) Abraham and Shaw, _Dynamics: The Geometry of Behavior_, v. I-III (strongly reccomended for foundations and pictures) Robert Devaney, _Chaotic Dynamical Systems_ (however I've heard bad things about this book's rigor, from a former colleauge of Devaney's and others) JM Thompson and Stewart, _Non-Linear Dynamics and Chaos_ We finally decided on the software packages DS-I and DS-II from Dynamical Systems Inc. (PO Box 35241, Tucson, AZ 85740, (602) 825-1331), which we will be running on a vanilla PS/50. We got the demo disk for $10 and were very impressed. The full system costs $550 and includes Adams and Runge-Kutta integrators w/noise addition; discrete maps w/noise; 2- and 3-D plotting with magnification, rotation, translation, and Poincare sections; color coding for velocity; data smoothing and interpolation; a delay-differential equation integrator; phase portraits; bifurcation diagrams w/blowups; spectral analysis; fractal dimension calculation; Lyapunov exponents; Eigen-values and -vectors; and other stuff I don't pretend to understand. It runs (theoretically) on any PC w/practically any graphics. We ran the demo on a vanilla AT w/float processor and VGA, and the performance was reasonable, the resolution could have been better. There is site licensing and quantity discounts. We currently plan two sections of the course, one mathematically oriented and requiring multi-variate calculus and diff. eq.; the other relatively non-mathematical, designed to expose the general student to the subject. In the first section we will work through most chapters of Edward Beltrami's _Mathematics for Dynamic Modeling_. In the second section we will be using Abraham and Shaw's series, as well as supplementary articles provided by the students and instructor. I will be focusing on getting a basic competence in the mathematics and concepts of the application of Dynamic Systems to Self-Organizing Systems and the relation between dynamics and symbolic behavior. I'll be studying Prigogine, Haken, fractal dimension, entropies of attractors, dissipative structures, phase changes, and whatever else I come across. Summary follows. My comments are in square brackets. ============================================================================ >From: Anand Rangarajan <anand%brand.usc.edu@oberon.usc.edu> To be more specific, phase transitions are possible only in very large systems (can treat averages statistically). Crystal growth is an example of a phase transition (equilibrium). What happens here is a sharp change in behavior after the ``transition'' point. One measure of collective action here is statistical correlations. The correlation length goes up drastically after a phase transition indicating that information has been communicated. This is similar to the action of a laser before and after its transition point. Before - it is just a lamp, after- there is increased coherence and resonance. However the laser is maintained far from equilibrium (so the transition has been dubbed a non-equilibrium phase-transition by Haken and his co-workers at any rate). Please see the chapter by Anderson (chap. 2 I think), in ``Emerging syntheses in science'', ed. by David Pines, Addison Wesley Publishing Co. Inc., 1988. Also, the first reference in that chapter is more technical (I don't have the book with me ) and the chapter by Charles Bennett in the same book. Also, a good intro to simulated annealing is ``Simulated Annealing, Theory and Applications'' by P.J.Van Laarhoven and Aarts (has discussion of phase transitions in annealing). The problem seems to me is the very definition of a SOS. If SOS refers to collective behavior, then eq. phase transitions can be included. If SOS is restricted to non-equilibrium then only non-eq. phase transitions can be included. But you are right- Dyn. Sys. is the general field and since a SOS is so vague, a lot of work needs to be done. [ Anand also recomends: _Self-Organizing Systems: the Emergence of Order_ ed. Eugene Yates; _From Equilibrium to Chaos_ by Rudiger Seydel as an introduction; Guck.+Holmes; and Eric Jantsch, _The Self-Organizing Universe_ ] ============================================================================ >From: Bruce Stewart <bstewart@bnlux0.bnl.gov> Organization: Brookhaven National Lab., Upton, N.Y. There is a book by Huseyin Kocak, published by Springer, which includes a nifty diskette for IBM-PC, price about $50. Jim Yorke will probably send you his PC software if you send him a blank diskette and perhaps a small fee. (Math Dept, U Maryland College Park). If you want the ultimate user interface and have access to a Silicon Graphics Iris workstation, I have some software which you can have for free. I plan to use it to help teach a course at Princeton this spring. ============================================================================ >From: cws@lab9.math.ufl.edu We bought Dynasim for the Math Department here on my recommendation and it wasn't worth the rather stiff price or the recriminations from my colleagues. (I hoped we could have some of the fun of the pictures in Abraham and Shaw.) Dynasim is copy-protected, not too versatile, and in spite of Ralph Abraham's claims that the integrator is dynamite stuff, has a tendency to draw closed orbits as open. We have been more impressed by a package called Tutsim (which is really aimed at engineering simulation, almost like an analog computer), which is sometimes advertised in Byte, and by the package Springer-Verlag peddles to accompany a text in ODE and dynamics. Both are much cheaper than Abraham's package. I can't remember the name of the Springer-Verlag package -- it was written at Brown for a course taught there, and it really draws things like the van der Pol closed orbit as *closed*, which is what one wants for pedagogy. The other package, Tutsim, got a lot of mileage put on it by a colleague fiddling with some systems of differential equations for his research, since he could readily tweak a value and re-run the experiment to see how stable his schemes and claims really were. Chris Stark Dept. of Mathematics University of Florida Gainesville, FL 32611 cws@mathlab.math.ufl.edu stark@pine.circa.ufl.edu stark@ufpine.bitnet ============================================================================ >From: J. Mailen Kootsey <jmk@cs.duke.edu> The National Biomedical Simulation Resource (an NIH funded research facility here at Duke) has written and distributes a simulation package called SCoP that should fill your needs outlined in your news item. SCoP runs on IBM PC's and clones, on VAXes under VMS, and on UNIX machines such as SUN's, VAXes, Pyramids, etc. We distribute the software in compiled and source form for a handling fee of $25 and it can be copied freely for educational or research use. You need a text editor of some sort to prepare the source files and a C compiler (we recommend Turbo-C on the IBM PC). If you will email a USMail address to me, I will send you a brochure with more details. SCoP is a versatile, interactive system designed to make powerful simulation techniques available with a minimum of programming knowledge and skills. The user supplies the model equations (algebraic, ODE's, or some types of PDE's; linear or nonlinear) and SCoP supplies the solver and the user interface -- control of the calculation, plotting the output or writing to disk, manipulation of parameters, etc. The program is menu driven with extensive on-line help. The package also includes a nonlinear optimizer for parameter estimation. You can readily do phase plots as you specified and include experimental or other external data in plots. SCoP can handle a wide range of problem sizes, from one or two state variables to tens of thousands or more -- depending mostly on the hardware it is run on. We are now distributing version 2.6 and are preparing version 3.0 for shipment in the next month or so to add some new features. Let me know if you would like to try SCoP. Mailen Kootsey Director, NBSR jmk@nbsr.mc.duke.edu [ I have technical literature on SCoP. It includes a number of integration and simultaneous equations methods, and forcing and stochastic functions. Basically, the way the system works is to generate data using the above methods, and then optimizing these results relative to some user-provided data set. Sensitivity analysis included. ] ============================================================================ >From: Federico Cuello <cuello@uxe.cso.uiuc.edu> With all the disclaimers that may apply, this is something that you may find interesting: In the last issue of MacWeek (16 November 1988) there is a note announcing the release of these two simulation programs: _Mac Analyst_: "A program for diagramming and analyzing complex systems. I has a lot of tools for simulating the information flows within a system and the process that acts on the data. The package supports 'diagram levelling', allowing processes on one diagram to be explo- ded with a double-click of the mouse into a more detailed lower-level diagram. _Mac Designer_: "A program for diagramming the structure of an information system and generating a textual description of such system". Both products are for the Apple Macintosh w/1 MB RAM. They are produced and marketed by: _Excel Software_\ P. O. Box 1414 Marshalltown, Iowa 50158 (515) 752 5359 at $795.00 each. The most important is the graphical systems-dynamic approach that they achieve, which would cost at least $10,000 to achieve on a Sun. For that price, you can get an Apple Macintosh SE with 4 MB RAM, a 25 Mhz. accellerator card and both simulation software packages (and still have some leftover to by the Mathe- matica program from Wolfram Research Inc.). cuello@uxe.cso.uiuc.edu (Federico Cuello) Research Assistant Department of Economics University of Illinois at Urbana-Champaign ============================================================================ >From: pacbell!pbhyg!ead@decwrl.dec.com Organization: Pacific * Bell, San Ramon, CA There's a text associated with DYNAMO that you may want to look at, which is fairly comprehensive in describing positive and negative feedback, rates and levels; KSIM is another software package which is unfortunately more primitive than DYNAMO. In the Mac world, there is STELLA. There was an article recently in Scientific American on chaos theory. Also, you may be interested in some of Prigogine's more recent work, which tends toward a treatment of time: titles like "An alternative to quantum theory" (1988), "Intrinsic irreversibility in quantum mechanics" (1987), "Poincare's theorem and unitary transformations for classical and quantum systems" (1988), "Irreversibility and space-time structure" (1987), "Order out of chaos" (1987), oops, that was 1984, reviewed several times in that year), "Exploring complexity" (1987), etc. Sounds like an interesting course. I'm math phobic, but I'm a researcher in the philosophy and history of the systems movement, with an emphasis on cybernetics. So I run across this stuff. I have a complete bibliography on Prigogine, if you want to know where to find anything mentioned above. Good luck, Elizabeth ============================================================================ >From: julian@riacs.edu Since you're going to be using Suns I'd recommend Mathematica from Wolfram Research Inc. It can handle everything you described in the posting; additionally, since it is general purpose, it will be able to handle other mathematical tasks as well. Dr. Julian "a tribble took it" Gomez 415/694-6363 julian@riacs.edu || {...decvax!}ames!riacs!julian RIACS - Research Institute for Advanced Computer Science [ I've asked for literature from Wolfram, but to date it has not arrived. ] ============================================================================ >From jfc@ATHENA.MIT.EDU Wed Nov 23 07:36:56 1988 Organization: Massachusetts Institute of Technology I am taking a course at MIT called "solar system dynamics". It is really about chaos. The professor has written a number of short programs, each of which generates a surface of section for a problem of interest (a surface of section is a two-dimensional cross section of 4 dimesnsional phase space [at least as we use it]). These run under X windows, but should be portable to other graphics. A PC/AT is a little slow, but a Sun should be fine (we run it on IBM PC/RTs and VS 2000s). The course has been mostly from his own notes, so I can't recommend any texts (he says there aren't any good ones, at least that overlap his course enough). This subject can lead to some interesting, and not obviously relevant, topics (for example, what is the "most irrational" number? This came up during the proof that a linearly stable system remains stable under perturbation). --John Carr (jfc@athena.mit.edu) [ I've asked John for more information, but have no reply yet ]. ============================================================================ >From: sunybcs!rutgers!cs.ucsd.edu!demers Organization: EE/CS Dept. U.C. San Diego If you need some more mathematical preliminaries, I think the Hirsch & Smale book, _Differential Equations, Dynamical Systems, and Linear Algebra (Academic Press, 1974) is excellent. I am not familiar with good software, I have used a product called Phaser, which plots phase maps. It's on a PC, and it's not really very good. I don't know where it comes from. Dave DeMers demers@cs.ucsd.edu Dept of Computer Science & Engineering UCSD La Jolla, CA 92093 ============================================================================ >From: peter@SGI.COM (peter broadwell) Organization: Silicon Graphics, Inc. Mountain View, CA A very nice set of software that I have some experience with is called CHAOS and comes from Brookhaven national labs. It runs on Silicon Graphics Iris's so it is able to give very nice dynamic displays of 3-D projections. Contact bstewart@bnl.gov regarding availability. Here is a blurb from a README in the system: ******************************************************************************* CHAOS - Version 2.0 Visual Dynamics Software Conceived by: Dr. Bruce Stewart Designed and Implemented by: Ed Thieberger & Bruce Stewart Last update - July, 1987 ******************************************************************************* Welcome to visual dynamics! DYNAMICAL SYSTEMS This software is designed to explore behavior of dynamical systems by computing their evolution in time and visualizing their orbits in phase space. Seven exemplary systems are included; each traces out orbits in a 3-d space. Each system can have different long-term qualitative behaviors, depending on values of control variables and initial conditions. To encourage exploration, these and other parameters can be conveniently changed using popup menus. -------------------- really nice stuff ;;peter@sgi.com [ See Bruce's comment above ]. ============================================================================ >From: jweiss@cgdra.UCAR.EDU (Jeffrey Weiss) Organization: NCAR/CGD, Boulder, CO Regarding your bibliography, the two texts that I find most useful and complete are Guckenheimer and Holmes; Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields; Springer-Verlag Lichtenberg and Lieberman; Regular and Stochastic Motion; Springer-Verlag. Both would be appropriate texts for a course in dynamical systems (and have been at Berkeley in the Physics Dept.) Of the two, G & H is more mathematical while L&L is more physical but not as well organized, which can make it confusing (at least I get confused sometimes). In addition, there are at least two collections of reprints that you may find useful: P. Cvitanovic, Universality in Chaos S-B Lin, Chaos (I'm not positive of the editor's name on this one) I hope you find this useful. In addition, I am interested in whatever information you obtain about software. Jeffrey Weiss jweiss@cgdra.ucar.edu ============================================================================ Reply-To: zqli@tcgould.tn.cornell.edu (Zhenqin Li) Organization: Cornell Theory Center, Cornell University, Ithaca NY [ On Prigogine, Haken, et al. ] I believe most physicists would consider the above theorizing as at best soft-core sciences, i.e., they are mostly philosophies rather than methods. You may check a book review in Physics Today around 1983 about "From being to becoming". It says the book contains either stuffs which are correct but not new, or stuffs which are new but wrong. I am not sure if this view is simply a prejudice of physicists. You may also look at a review article in November 1988 issue of "Physics Today" entitled "Chaos: How Regular can it be?" by a group of Russian physicists, including Roald Z. Sagdeev, the drector of Space Research Institute. For Supplementary References, I think you might want to add one about Cellular Automata, which complements with continuous approach to the dynamic systems, the following reference may not be the best one: Stephen Wolfram, Physical Review letters Vol.54, 735 (1985). By the way, you might also want to know about Wolfram's software Mathematica by calling (217)398-0700. -- Zhenqin Li (607) 255-0556 (O) | "No man is an island." -John Donne ============================================================================ >From: fishwick@uflorida.cis.ufl.EDU (Paul Fishwick) Organization: UF CIS Department I suggest that you look into the package DESIRE if you are looking for something inexpensive which is a truly powerful ODE package for an IBM PC. I am teaching my advanced simulation course next semester and I am using "Interactive Dynamic System Simulation" by Granino Korn, for the 'continuous' part of the course - there is a combination, shrink- wrapped version ISBN 0-07-852261-7 (book and disk) from McGraw Hill. MAKE SURE to ask for the "Professional Series" book division -- the normal textbook division did not know about it. It is brand new: 1989 copyright. A caveat: It is not a textbook (no exercises) but it seems much more than a user's manual for DESIRE. I intend to lecture concepts, theory, and methodology in class (from other books - your choice of Beltrami seems a good one) and then have give assignments that use DESIRE. Hopefully, this will give the students the right blend of theory and practice. >Requirements: > ODE solutions, trajectories, phase space projections, > bifurcation diagrams. DESIRE can handle all of these very nicely. There are no special facilities for 'zooming' on iteratively defined sets such as Julia, Mandelbrot,etc. but the 'plot' function can be easily rigged for plotting in real or complex space. NOTE: the book version of the software is complete DESIRE EXCEPT for a limit of 5 first order DE's (which should not be a problem for many demonstrable systems), and a limit on the array size for FFT. DESIRE handles general matrix operations, convolution, FFT in addition to DE's. >Desired: > Decent user interface, plot from data imported from text files, > generality, speed, resolution. I am very impressed by the speed and it is very interactive. Parameter adjustments are easily done without re-compiling. It is an extremely easy to use and flexible system. Here is an example non-linear system (Lorenz System) set up for an XY plane view - note the ease of writing the equations: DT=.01 | TMAX=50.0 | NN=5000 x=2 | y=2 | z=2 | scale=30 drun DYNAMIC d/dt x=10*(y-x) | d/dt y=x*(28-z)-y | d/dt z=x*y-2.67*z dispxy x,y | -- display XY plane >Price and Licensing: > Not so sure here. We can probably get a few hundred bucks > together, and obviously academic discounts and liberal licensing > are preferred. If the student buys the book/disk (which I think is around $40) then you're set! Hope this helps --- I'd also like to hear from others about their packages for both continuous and discrete systems simulation. -paul +------------------------------------------------------------------------+ | Prof. Paul A. Fishwick.... INTERNET: fishwick@bikini.cis.ufl.edu | | Dept. of Computer Science. UUCP: gatech!uflorida!fishwick | | Univ. of Florida.......... PHONE: (904)-335-8036 | | Bldg. CSE, Room 301....... FAX is available | | Gainesville, FL 32611..... | +------------------------------------------------------------------------+ [ I really should check this one out more thoroughly . . . ] ============================================================================ >From: dm@bbn.com (Dave Mankins) Organization: BBN Laboratories Incorporated, Cambridge, MA In article <1934@crete.cs.glasgow.ac.uk> jack@cs.glasgow.ac.uk (Jack Campin) writes: > >What about adding "Catastrophe Theory" by Vladimir Arnol'd (Springer-Verlag) >as a counterweight? I thought there was something wrong with my brain when >reading Thom ("this stuff seems like gibberish...") and Zeeman mostly follows >the Thom line. Arnol'd gave me the welcome reassurance that it was indeed >gibberish. For a decent middle ground, accessible to those of us who read popular math books on the bus, you might also look at the well-written, entertaining, _Mathematics of the Unexpected_, by Ivar Peterson. Peterson's work looks at both catastrophe theory and chaotic dynamics theory. For chaos theory, it is a MUST READ supplement for James Gleick's book, _Chaos_. Reading Peterson makes you distinctly aware of Gleick's shortcomings in describing the research he reports on (Peterson is a mathematician who writes (wonderfully), not a science writer who understands math (passably)). For catastrophe theory, the book is about at the same level of Arnold's book, but takes a middle ground. Its outlook is: these are the basic results of catastrophe theory, they are interesting, but their significance is mostly exaggerated. It has an interesting final chapter that ties in Homer's _Illiad_ and _Odyssey_ in a non-contrived manner. Still, Arnold's book has some truly fine invective in it, and is worth reading for that alone. -- david mankins/dm@bbn.com ============================================================================ >From: tomp@hpsrli.HP.COM (Tom Parker) Organization: HP Network Measurements Div, Santa Rosa, CA I can recommend (with no impartiality attempted) two references and one software package. The first reference is "Chaos: A Tutorial for Engineers" by Parker and Chua in the August 1987 issue of the Proceedings of the IEEE. This is a tutorial paper covering limit sets, stability, invariant manifolds, Lyapunov exponents, dimension, and reconstruction of attractors. It contains theory as well as numerical algorithms. The second reference is the book "Practical Numerical Algorithms for Chaotic Systems" by Parker and Chua to be published by Springer-Verlag in April/May 1989. It is a more detailed, expanded version of the tutorial. Additional topics include bifurcations, bifurcation diagrams, phase portraits, and numerical integration. The software package is called INSITE. It runs on the X11 graphics package under UNIX and on the MetaGraphics graphics package under PC-DOS. There is a short write-up on it in the August 1987 issue of the Proceedings of the IEEE. It contains graphically based, interactive programs that calculate and plot trajectories and orbits, calculate and plot bifurcation diagrams of continuous- or discrete-time systems, calculate Lyapunov exponents (via simulation), calculate correlation dimension of attractors (from a data file obtained via experiment or simulation), calculate and plot one-dimensional invariant manifolds of a (Poincare) map, calculate and plot periodic solution of continuous- or discrete-time systems, and calculate and plot phase portraits of two-dimensional continuous-time systems. The software will be available for distribution in June, 1989. The cost will be around $200. The complete source code is included. Ordering information on the software can be obtained by writing INSITE P.O. Box 9662 Berkeley, CA, 94709-9662 tom parker [ I would but it's just too late for us ]. ============================================================================ >From: cheryl@tcgould.tc.cornell.edu (cheryl) Organization: Cornell Theory Center, Cornell University, Ithaca NY Birkhoff and Rota: Good for a first course in ODEs. Greens functions, Bessels equation, harmonic oscillator, eistence and uniqueness, power series solutions, stuff like that. a RED book from Wiley + Sons, 1978. Hirsch and Smale: Good for intermediate ODEs, dynamical systems, an IDEAL background for Guck.+Holmes. I would recommend this even if you've had a course or two in ODEs. A GREEN book from Academic Press. Gukenheimer and Holmes: Number 42 in the Springer series on Applied Mathematical Sciences, this is, in fact, the answer to the ultimate question of life, the universe, and everything. A YELLOW book from Springer, 1983. Cheryl ============================================================================ >From: jdm@emx.utexas.edu (James Meiss) Organization: UTexas Department of Physics There is a nice book by Devaney, called Dynamical Systems or something that goes through alot of the proofs. Also check out the reprint collections edited by Cvitanovic "Universality in Chaos" published by Adam Hilgar, and a similar one by Hao Bao Lin, World Scientific Press. Finally, if you get interested in Hamiltonian Systems there is a great new reprint collection "Hamiltonaian Dynamical Systems" edited by MacKay and Meiss** also published by Adam Hilgar. You can get it from their US distributor, Taylor-Francis (New York). Jim Meiss jdm@emx.utexas.edu jdm%uta.MFENET@nmfecc.ARPA **bias is obvious here! ============================================================================ >From: cosell@bbn.com (Bernie Cosell) Organization: Bolt Beranek and Newman Inc., Cambridge MA Try "Chaos", edited by Arun Holden, Princeton U Press. 1986 I think you'll find that it has all the meat the Gleick skipped over. ============================================================================ End of summary -- O----------------------------------------------------------------------> | Cliff Joslyn, Cybernetician at Large | Systems Science, SUNY Binghamton, vu0112@bingvaxu.cc.binghamton.edu V All the world is biscuit shaped. . . ------------------------------ +--------------------------+ | END OF SIMULATION DIGEST | +--------------------------+