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  • Roger L. Bagula
    ... Subject: Subject: ARTICLES - Part (1/5) of UK Nonlinear News Date: Wed, 01 Sep 2004 15:27:45 +0100 From: UK Nonlinear News
    Message 1 of 2 , Sep 1, 2004
      -------- Original Message --------
      Subject: Subject: ARTICLES - Part (1/5) of UK Nonlinear News
      Date: Wed, 01 Sep 2004 15:27:45 +0100
      From: UK Nonlinear News <uk-nonl@...>
      Organization: UCL Centre for Nonlinear Dynamics
      Newsgroups: sci.nonlinear

      Subject: ARTICLES - Part (1/5) of UK Nonlinear News

      UK Nonlinear News, August 2004


      Articles and Reviews

      * Book Review: Simulating, Analyzing, and Animating Dynamical
      Systems. A
      Guide to XPPAUT for Researchers and Students .
      Reviewed by Harvinder Sidhu.
      * Book Review: Critical Phenomena in Natural Sciences. Chaos,
      Selforganization and Disorder: Concepts and Tools .
      Reviewed by Henrik Jensen.
      * Boor Review: Weighing the Odds: A Course in Probability and
      Reviewed by Jaroslav Stark
      * Book Review: Nonlinear Dynamics in Physiology and Medicine
      Reviewed by Alona Ben-Tal
      * Report: Noisy Oscillators - Workshop on the Dynamics of Coupled
      Oscillatory & Complex Systems
      By Peter V.E. McClintock
      * Report: Modelling of Neuronal Dendritic Trees
      By Yulia Timofeeva
      * A listing of reviews of nonlinear books can be found at

      (this article is periodically updated).
      * An index of UK Nonlinear News can be found at



      Simulating, Analyzing, and Animating Dynamical Systems. A Guide to
      for Researchers and Students

      Bard Ermentrout

      Reviewed by Harvinder Sidhu

      SIAM. Softback, 290 pages.
      ISBN: 0-89871-506-7.

      Researchers in diverse areas such as Biology, Physics, Engineering etc
      constantly investigating nonlinear phenomena in order to understand the
      behaviour of their specific physical system. Furthermore, nonlinear
      is now an integral part of many undergraduate Mathematics and Physics
      curricula in universities all over the world. Summer schools in areas
      as ecology, physiology, medicine etc have also devoted much time to
      exploring nonlinear phenomena. Regardless of the application, the most
      important issue in the understanding of nonlinear behaviour is the
      combination of both analytical and computational techniques. However, a
      significant number of researchers and students from these diverse fields
      have insufficient computational background to program in MATLAB, MAPLE,
      MATHEMATICA etc to solve the governing equations for the system that
      are modelling. This is where XPPAUT is extremely useful. Bard
      the author of this book and the developer of the software, states that
      XPPAUT offers several advantages over the above-mentioned softwares.

      * a simple syntax for setting up various systems of equations such as

      ODEs, maps and some PDEs,
      * a convenient interface with AUTO - a powerful continuation and
      bifurcation package,
      * free downloading of the source code.

      I must concur with Bard regarding the advantages of XPPAUT and see these
      compelling reasons for anyone interested in studying nonlinear dynamics
      use this software. Personally I feel that XPPAUT is an excellent
      for both researchers and students. Prior to reviewing this book, I have
      always used MATLAB and AUTO in my research. However, I am now a
      and have begun to use XPPAUT extensively in both my research and
      teaching of
      dynamical systems. I must now stop talking about the software and
      proceed to
      review this book, although I find it very difficult to divorce one from

      The book consists of nine chapters and seven appendices. The author is
      to be
      commended for his excellent organization of the subject matter and his
      clarity in writing. I found the background of the physical models used
      illustrate particular aspects of XPPAUT to be extremely refreshing.
      contrived examples are often used in books, this is not the case here.

      The author begins with a useful explanation of how to install the
      package on
      computers with various operating systems. Chapter 2 explains the basics
      creating an ODE file and solving the system and plotting the solutions.
      to the simplicity of the package, chapter 2 provides the reader with
      sufficient information to analyse their own system using XPPAUT. Chapter
      provides a more detailed explanation of the syntax of the ODE files.
      the author explains how to set up user-defined functions as well as the
      handling of discontinuous differential equations in XPPAUT. Chapter 4
      is aptly entitled ``XPPAUT in the Classroom'' is one of the most useful
      chapters in the book. The chapter begins by showing how XPPAUT can be
      to plot functions, before focussing on one-dimensional maps. Here the
      shows how to obtain cobweb diagrams, bifurcation diagrams, liapunov
      exponents, and the devil's staircase for such maps. The final part of
      chapter is dedicated to nonlinear differential equations. The author
      explains very clearly how three- and higher-dimensional dynamical
      can be analysed using this package. Chapter 5 explains how to define ODE

      files for ``more complicated model systems'' such as systems with delay,

      integral equations, stochastic equations and differential algebraic
      equations. Chapter 6 focuses on the use of XPPAUT to solve boundary
      problems and special cases of spatially distributed systems. I was very
      impressed with the ease with which the governing equations can be set up
      such systems using XPPAUT. Chapter 7 is one of the major chapters as it
      clearly explains how to use XPPAUT's simple interface to the
      package AUTO. Although I have previously used AUTO, I found the XPPAUT's

      interface much easier to use. Animating systems is the focus of chapter
      Even I was able to produce good quality animations for some of my
      systems by
      following the author's clear step-by-step instructions and examples.
      Finally, chapter 9 is aptly entitled ``Tricks and Advanced Methods'' as
      provides users with very useful tips including exporting data, linking
      external C routines, and numerous other ways in which ``tricky'' systems
      situations can be handled.

      Overall I believe that this is an excellent book for researchers and
      students who are interested in learning how to analyse dynamical systems

      using XPPAUT -- a powerful, simple-to-use and free software package. By
      using this book readers will be able to discover the software's full
      of capabilities, and like me, they will certainly be impressed.

      UK Nonlinear News would like to thank SIAM for providing a review copy
      this book.


      Critical Phenomena in Natural Sciences. Chaos, Fractals,
      and Disorder: Concepts and Tools

      By Didier Sornette.

      Reviewed by Henrik Jensen

      Springer, 2nd ed. 2004, 102 figs, 528pp., EUR 79.95, GBP 61.50, US $
      Hardcover, ISBN 3-540-40754-5

      This is an extremely impressive and comprehensive review of large areas
      research into the collective behaviour of systems with many degrees of
      freedom. The author, Didier Sornette, is an exceptionally productive
      researcher who has contributed to most of the topics covered in the
      This doesn't by any means imply that the presentation is limited to
      Sornette's own work. On the contrary vast numbers of models and
      are discussed in remarkable detail. The reference list contains a
      1067 items. One gets the impression that Sornette knows these references
      and out and presents the reader with a digested explanation of the
      content of this huge list of papers and books.

      The book does what the title promises, namely equip the reader with an
      arsenal of concepts and tools which will be a great help when reading
      research literature or attacking research problems in the field of, what
      might call, applied statistical mechanics. The focus is - again as the
      implies - on the correlated behaviour of systems with many components.
      term criticality is meant to imply that essential correlations exist
      the different parts of the system and, hence, its behaviour cannot be
      deduced by a simple summation of the properties of the individual

      The tools and concepts supplied include a basic and worthwhile
      to statistics. The first chapter introduces the very foundation of
      probability theory with a refreshing discussion of the frequency
      interpretation contrary to the Bayesian school. The material is
      organised in
      an unusual but very effective manner with an emphasis on characteristic
      functions, moments and cumulants. I like very much the discussion of
      Value Statistics and Large Deviations in Chap. 1 and 3 sandwiching the
      obligatory discussion of the Central Limit Theorem in Chap. 2. The
      peculiarities of power law distributions (Levy Laws) are detailed in
      4, Fractals and Multifractals are explained with great lucidity in Chap.
      Chap. 6 rounds off the mathematical tool box with a discussion of
      Rank-Ordering Statistics and Heavy Tails, topics which are central to
      current activities in complex systems research.

      The remaining 11 Chapters are concerned with physics concepts and
      models. A
      broad range of very relevant topics are covered: the relevance of the
      temperature concept to out-of-equilibrium systems, the role of
      correlations and phase transitions. The latter is the prototype example
      macroscopic coherent behaviour in physics; here the concept and its
      mathematical description are explained at a level that should be
      to readers with no physics background. Two more methods chapters follow:
      from dynamical systems theory on bifurcations and one from statistical
      mechanics on The Renormalisation Group.

      Chaps. 12 and 13 present two important models: The percolation model
      is a paradigmatic model from statistical mechanics and the Rupture
      which is an interesting model with a special appeal to materials
      and geo-physicists. Chap. 14 and 15 contains probably the material with
      widest current appeal and inspiration. Back in 1987 Bak, Tang and
      published a paper in which they introduced the concept of Self-Organized

      Criticality which they suggested to be the generic explanation of the
      laws characterising many natural phenomena. This inspired a huge
      effort which is still very active. Sornette devotes Chap. 14 to a
      discussion of a large number of mechanisms that may lead to power laws
      focus next on specific Self-Organized Criticality models in Chap. 15. I
      these two chapters to be very useful nearly up-to-date summaries of the
      present research situation.

      The book's two last chapters contains for completeness discussions of
      systems. Again well introduced and well explain material.

      This book is a treasure horn. Without assuming much mathematical
      Sornette manages to supply the reader with the most essential
      tools and scientific concepts to be able to participate in the current
      research effort on developing mathematical modelling and understanding
      extended system in which the behaviour is a result of cooperative
      interaction between the components. A very good book to have in the bag!

      This is the second edition and it is even by Springer, it therefore
      surprises me that there are small mistakes here and there. None of these
      essential; a few might cause momentarily confusion for the reader
      with the material - I wonder if the copy editing has been sufficiently
      careful? Last point, do we use British or American spelling? Or both
      perhaps? I found on p. 96 line 9 and 11 a certain amount of oscillation
      between the two conventions. This is of course not important, but nor is


      Weighing the Odds: A Course in Probability and Statistics

      D. Williams

      Reviewed by Jaroslav Stark

      Cambridge University Press 2001, 0-521-00618, 566 pages.
      £26 (paperback); £75 (hardback)
      ISBN: 0-521-80356

      As those who have read some of my other book reviews in UK Nonlinear
      will know, one of my key concerns about the state of the mathematical
      sciences today is the gulf that exists between applied mathematics and
      statistics. I find it astonishing that someone can get a 1st class
      degree in
      Applied Mathematics from almost any university in the UK (and most other

      countries) but when confronted by real data will have practically no
      how to compare it to a mathematical model. Conversely, modern statistics

      concentrates primarily on developing ever more sophisticated techniques
      fitting and comparing models which from an applied mathematics
      (and particularly from a nonlinear dynamics point of view) are rather
      simplistic. As a consequence, ask either an applied mathematician or a
      statistician how to fit data to a set of coupled nonlinear differential
      equations and, with a few notable exceptions, you are likely to be met
      by a
      puzzled shrug of the shoulders.

      I was thus intrigued to find a close parallel in the mischievous first
      sentence of the volume under review:

      Probability and Statistics used to be married; then they
      separated; then they got divorced; now they hardly ever see each

      The book?s stated aim is to provide support for a much-needed
      reconciliation. As a, perhaps unintended, by-product the book?s unusual
      approach and entertaining style results in an introduction to statistics

      which is unusually accessible to an applied mathematics audience. As an
      added bonus, the final chapter on quantum probability and computing will
      of interest to anyone with a physics background. I doubt that there is
      another book anywhere that manages to combine topics as diverse as ANOVA
      quantum entanglement in such an effortless way. Essentially no prior
      knowledge is assumed in either probability or statistics, resulting in a

      work that is suitable for a very wide range of backgrounds.

      Given the author?s background, the underlying emphasis is on concepts in

      probability, ranging from an intuitive first introduction to topics as
      advanced as martingales. This gives the volume a strong mathematical
      flavour, with analysis and linear algebra playing a key role.
      ideas are introduced gradually, and the author maintains a balance
      the traditional frequentist approach and the Bayesian point of view. I
      suspect that he himself is more inclined philosophically towards the
      but he is not above criticizing a pure Bayesian methodology where
      appropriate. One interesting aspect is his strong dislike of hypothesis
      testing, and preference for reporting confidence intervals of estimated
      parameters instead. This is a point of view that I increasingly sense in

      modern statistics, and it is useful to have it argued here so

      A variety of other thought provoking and probably controversial ideas
      sprinkled throughout the book, always presented in a lively and
      manner. This makes for a very readable book, from which I learned a
      deal and into which I have been continuously dipping since I finished
      it. I
      would recommend it to anyone, from final year undergraduate, to an
      established researcher in nonlinear science. They might be surprised how

      interesting statistics can be, and perhaps respond more positively next
      they are asked to fit data to a model.

      UK Nonlinear News would like to thank Cambridge University Press for
      providing a copy of this volume for review.


      Nonlinear Dynamics in Physiology and Medicine

      Ann Beuter, Leon Glass, Michael C. Mackey and Michèle S. Titcombe

      Reviewed by Alona Ben-Tal

      Springer-Verlag, Interdisciplinary Applied Mathematics, Volume 25, 2003,
      pages, 162 illustrations, Hardcover.
      ISBN: 0-387-00449-1

      I was delighted when the book "Nonlinear Dynamics in Physiology and
      Medicine" arrived in the mail. This pleasant looking book is the most
      volume of the Interdisciplinary Applied Mathematics series by
      Springer-Verlag and since I know some other books in this series (for
      example, [1], [2], [3]) I looked forward to reading this new addition.

      The book has evolved out of notes written in three summer schools
      by The Centre for Nonlinear Dynamics in Physiology and Medicine at
      University. The summer schools were held in 1996, 1997 and 2000. The
      is an edited book with 12 contributors (mentioned later) that contains
      cutting edge subjects of research and (perhaps not surprisingly)
      mainly the work done by the McGill group.

      Chapter 1, by M. C. Mackey and A. Beuter, gives "A wee bit of history to

      motivate things". The chapter contains some interesting examples showing
      role mathematics has played in the life sciences and vice versa (but see

      also: highlights of a keynote address by Dr. Joel Cohen "Mathematics Is
      Biology's Next Microscope, Only Better; Biology Is Mathematics' Next
      Physics, Only Better." http://www.bisti.nih.gov/mathregistration/ ).

      Chapter 2, by J. Bélair and L. Glass, "Introduction to Dynamics in
      Difference and Differential Equations", has nice examples of nonlinear
      phenomena seen in physiological systems, among them, the co-existence of
      stable states in the human heart. Overall it is a reasonable
      introduction to
      the field but I was disappointed to find the following statement (given
      p. 17 when the authors discuss the period three window seen in the

      ..."So why did Li and Yorke (1975) claim "period three implies chaos"?
      and York 1975). The answer lies in the definition of chaos. For Li and
      Yorke, chaos meant an infinite number of cycles ....That definition does
      involve the stability of the cycles."

      In the context of the book it is not clear that "claim" actually means
      "proved" [4]. I also thought that for the purposes of the book it would
      been sufficient to give an intuitive definition of chaos, as the authors
      on p. 16, skip the exact definitions of chaos altogether and refer the
      reader to a technical definition of chaos, given for example in [5, 6].
      isn't this an example where mathematics is a better microscope? We KNOW
      an unstable chaotic solution exists even though we cannot observe it. I
      that a student reading this statement (and others on the definition of
      chaos) may get the wrong impression that only the observable solutions
      important (and see for example, [7]).

      Chapter 3, by M. R. Guevara, is another introductory chapter to
      dynamics and contains some very nice examples of non-linear phenomena in

      physiology. Chapter 4, also by M. R. Guevara gives a nice introduction
      the Hodgkin-Huxley equations and serves as a specific example to
      the subjects covered in Chapter 3.

      Chapter 5, by L. Glass looks at periodic solutions and the phenomena
      when an oscillating autonomous system is forced by a single stimulus or
      periodic train of stimuli. A related subject, "Reentry in Excitable
      is presented in Chapter 7 by M. Courtemanche and A. Vinet. Chapter 7
      describes the dynamics of excitable cardiac cell by three families of
      models: Cellular Automata, delay equations and partial differential

      The important subject "Effects of Noise on Nonlinear Dynamics" is
      covered in
      Chapter 6 by A. Longtin. Different kinds of noise are discussed.
      Postponement of a Hopf bifurcation is demonstrated in a first order
      equation (model for a pupil light reflex) and the phenomenon of
      phase locking (usually known as "skipping") is described. The phenomenon
      bursting as a result of noise is also presented but, to my
      there is no discussion (or even mention) of bursting without noise.

      It seemed natural to me to read next Chapter 9 by J. Milton. This is a
      chapter that describes the pupil light reflex. I thought that there is a

      good balance here between physiology and mathematics but there is a
      relatively large number of typos.

      I next read Chapter 10 by A. Beuter, R. Edwards and M. S. Titcombe
      describing the interesting phenomenon of tremor (an approximately
      movement of a body part). I thought it was interesting that the Van der
      equation was proposed as a model for Parkinsonian tremor but there is
      any discussion at all about this model. A six-unit Hopfield-type neural
      network model is discussed here in more detail.

      Finally, I made my way through the jargon of Chapter 8 (granulopoiesis,
      erythroid precursors, erythropoietin, neutrophil, am I reading English?,

      megakaryocytic, eosinophil, reticulocyte, idiopathic, promyelocytes, the

      list goes on, see http://cancerweb.ncl.ac.uk/omd/ for an On-Line Medical

      Dictionary). Chapter 8 by M. C. Mackey, C. Haurie and J. Bélair
      the control of blood cell production. Here you can find more examples of

      periodic behaviour on the scale of days that arise from Hopf
      bifurcations in
      delay equations.

      Throughout the book experimental results are presented and the authors
      with the readers the joys and sorrows of dealing with real data
      some practical aspects of estimating parameters (for example, a useful
      on obtaining data from published graphs by using Ghostview is given in
      Chapter 8 p. 248). All the chapters contain computer exercises with
      codes and data files that are available on line at
      http://www.cnd.mcgill.ca/books_nonlinear.html. The book also has three
      appendixes (an introduction to XPP, an introduction to Matlab and time
      series analysis) which I found handy. But the book lacks the coherence
      general perspective that a single authored book has (despite the noted
      effort by the authors). Still, this is a stimulating book. I don't
      it as a text book but certainly as a research and teaching resource.

      UK Nonlinear News would like to thank Springer-Verlag for providing a
      of this volume for review.


      1. J. Keener and J. Sneyd, "Mathematical Physiology", Springer-Verlag,

      2. J. D. Murray, "Mathematical Biology I. An Introduction",
      Springer-Verlag, 3rd edition, 2002.
      3. R. Seydel, "Practical Bifurcation and Stability Analysis. From
      Equilibrium to Chaos", Springer-Verlag, 2nd edition, 1994.
      4. T-Y Li and J. A. Yorke, "Period Three Implies Chaos", The American
      Mathematical Monthly, Vol. 82 (10), 1975, pp. 985-992.
      5. S. Wiggins, "Introduction to Applied Nonlinear Dynamical Systems
      Chaos", Texts in Applied Mathematics, Springer-Verlag, 2nd edition,

      6. M. W. Hirsch, S. Smale and R. L. Devaney, "Differential Equations,
      Dynamical Systems & An Introduction to Chaos", Elsevier, 2nd
      7. C. Robert, K. T. Alligood, E. Ott and J. A. Yorke, "Explosions of
      Chaotic Sets", Physica D, Vol. 144, pp. 44-61, 2000.


      Noisy Oscillators: Workshop on the Dynamics of Coupled Oscillatory &

      Ljubljana, 10-13 December 2003

      By Peter V.E. McClintock

      The Workshop on the Dynamics of Coupled Oscillatory and Complex Systems
      held at the University of Ljubljana, Slovenia, 10-13 December 2003. The
      venue was the Zborni?na dvorana in the historic central building of the
      University in the middle of the city, a stone's-throw from the
      where Mahler worked for many years (and Beethoven's job application was

      This was a small select gathering, mostly by invitation, and highly
      interdisciplinary. The 37 participants, drawn from 17 countries,
      all ages and stages from selected PhD students up to senior scientists.
      meeting was opened by Professor Katja Breskvar, Vice-Rector of the
      University of Ljubljana. Professor Toma? Slivnik, Dean of its Faculty of

      Electrical Engineering, contributed some further welcoming remarks and
      first scientific session then followed immediately.

      The meeting reflected the fact that, in the modern theory of complex
      dynamical systems in physics (fluctuations in lasers), biology
      (transport of
      proteins), physiology (autonomous nervous control of the cardiovascular
      dynamics), and econometrics the effects of both chaotic and stochastic
      dynamics, and their mutual interactions, must be taken fully into
      It was also motivated by a growing awareness that reaching an
      of the general features of chaos-noise interactions in complex dynamical

      systems may introduce entirely new ideas of how to control the system
      dynamics, and of how to exploit its complexity usefully in a variety of
      applications on all scales from molecules to the global economy.
      discussed were numerous, including e.g. applications of stochastic
      and Brownian ratchets in biology, chaotic communications, and chaos
      All these systems operate in regimes far away from thermal equilibrium,
      the problems of modelling are highly challenging.

      The function of the meeting was thus to bring together fluctuational
      dynamicists working on nonequilibrium and complex systems to engage in
      direct discussions with experimental scientists working in areas that
      potentially be described by the theories that are under development,
      especially in biology. It was felt to have succeeded admirably in these
      aims. The sessions on cardiovascular dynamics were especially valuable,
      data obtained in Lancaster, Ljubljana, Oslo and Pisa being exposed to
      general scrutiny and open discussion with theorists expert in e.g.
      stochastic dynamics, synchronisation, information theory, relaxation
      oscillations, excitable systems and physiology.

      The local Director, Professor Aneta Stefanovska did a superlative job in

      organising all aspects of the meeting { both scientific and social { the

      latter including a tour of central Ljubljana, two excellent concerts, a
      magnificent conference dinner and, after the conference, an excursion
      in Cerknica (the "disappearing lake"), the Postojna caves, a
      and another memorable dinner. The meeting was supported by INTAS and by
      European Science Foundation under its STOCHDYN programme.

      Details can be found on the conference web page:


      Report: Modelling of Neuronal Dendritic Trees

      ICMS, 14 India St, Edinburgh, 18 June 2004

      By Dr Yulia Timofeeva

      A one-day meeting on Modelling of Neuronal Dendritic Trees was held on
      Friday 18th June at 14 India St. Edinburgh, the birth place of James
      Maxwell and home to the International Centre for Mathematical Sciences.

      Organised by Dr Stephen Coombes (Nottingham) and Dr Gabriel Lord
      (Heriot-Watt), the workshop focused on the application of mathematical
      from modelling and numerical analysis to information processing and
      within a single neuron with branched dendritic structure. The meeting
      brought together around 40 researchers in computational neuroscience,
      applied mathematics and the life sciences.

      Professor John Rinzel (Center! for Neural Science, NYU), started the
      by giving a thorough background about the compartmental method and the
      seminal contributions of Wilfrid Rall. He emphasised a minimalistic
      to investigating dendritic cable properties using only a few
      spatial/electrical compartments. Using a comprehensive compartmental
      simulation study, Dr Arnd Roth (UCL) then explained the link between
      dendritic morphology and the experimentally observed patterns of forward
      backward propagating action potentials seen in real neurons. The
      of mathematical analysis was highlighted by the talk of Professor Steve
      (Rice University, Texas), who described a rigorous approach for
      the location and time course of synaptic input from multi-site potential

      recordings. Dr Mickey London (UCL) ill ustrated the success of
      theory in uncovering the role of dendritic structure in neuronal
      and Dr Bruce Graham (Stirling University) spoke about dynamics of
      integration in a hippocampal pyramidal neuron model. Some new
      ideas in compartmental modelling were introduced by Dr Ken Lindsay
      and the meeting concluded with a talk by Dr David Barber (IDIAP,
      Switzerland) on a mathematical framework for learning with dendritic

      Overall the workshop was very successful, with a large attendance,
      presentations and fruitful discussions. The meeting was financially
      supported by the ICIAM99 fund.


      Issue 37, WWW -
      Aug 2004 Email submissions -

      Respectfully, Roger L. Bagula
      tftn@..., 11759Waterhill Road, Lakeside,Ca 92040-2905,tel:
      619-5610814 :
      URL : http://home.earthlink.net/~tftn
      URL : http://victorian.fortunecity.com/carmelita/435/
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