Nonlinear Phenomena in Physics and BiologyRichard H. Enns The Advanced Study Institute (ASI) on Nonlinear Phenomena-in Physics and Biology was held at the Banff Centre, Banff, Alberta, Canada, from 17 - 29 August, 1980. The Institute was made possible through funding by the North Atlantic Treaty Organization (who sup plied the major portion of the financial aid), the National Research and Engineering Council of Canada, and Simon Fraser University. The availability of the Banff Centre was made possible through the co sponsorship (with NATO) of the ASI by the Canadian Association of Physicists. 12 invited lecturers and 82 other participants attended the Institute. Except for two lectures on nonlinear waves by Norman Zabusky, which were omitted because it was felt that they already had been exhaustively treated in the available literature, this volume contains the entire text of the invited lectures. In addition, short reports on some of the contributed talks have also been included. The rationale for the ASI and this resulting volume was that many of the hardest problems and most interesting phenomena being studied by scientists today ar.e nonlinear in nature. The nonlinear models involved often span several different disciplines, °a simple example being the Volterra-type model in population dynamics which has its analogue in nonlinear optics and plasma physics (the 3-wave problem), in the discussion of the social behavior of animals, and in biological competition and selection at the molecular level. |
Contents
| 20 | |
Particle Physics to the Present | 28 |
INVERSE SCATTERING TRANSFORM THEORY | 36 |
D | 42 |
C | 48 |
D | 67 |
Remarks on Nonlinear Evolution Equations and | 83 |
The Linearity of Nonlinear Soliton Equations | 95 |
Nonlinear Waves in Neuronal Cortical Structures | 369 |
I | 371 |
PREVIOUSLY PROPOSED THEORIES | 382 |
Bifurcations in Insect Morphogenesis I | 401 |
I | 403 |
MODELS OF POSITIONAL COORDINATE SYSTEMS | 412 |
IV | 430 |
68 | 448 |
Numerical Computation of Nonlinear Waves | 157 |
Bifurcations Fluctuations and Dissipative Structures | 185 |
III | 189 |
IV | 196 |
Chemical Oscillations | 197 |
CLASSICAL STABILITY ANALYSIS | 205 |
the Schlögl Model | 211 |
37 | 215 |
BIFURCATION ANALYSIS | 223 |
54 | 308 |
Models in Neurobiology | 345 |
Bifurcations in Insect Morphogenesis II | 451 |
Selection and Evolution in Molecular Systems | 485 |
MOLECULAR SELFREPLICATION | 487 |
Escape from Domains of Attraction for Systems Perturbed | 549 |
Seminars | 567 |
On Some Nonlinear Schrödinger Equations | 577 |
Nonlinear Superposition of Simple Waves in Nonhomogeneous | 587 |
| 601 | |
| 606 | |
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Common terms and phrases
Ablowitz action potential amide-I amplitude analysis apposed approximation asymptotic axon Bäcklund transformation behaviour Belousov-Zhabotinskii reaction boundary conditions branches cells chemical coefficients concentration constant convex set coordinate corresponding critical point differential equations diffusion dimensional distal Drosophila Drosophila melanogaster duplicate dynamics eigenfunction eigenvalue equilibrium evolution equations extracellular finite fluctuations Fokker-Planck equation fragment function gradients high point hypercycle imaginal discs initial conditions integral interaction inverse scattering Kaup limbs limit cycle linear macroscopic master equation Math mathematical mechanisms membrane potential method mode mutants neurons Nicolis nonequilibrium oscillations parameter pattern periodic solutions perturbation phase phenomena Phys physical plane polar polynucleotide potassium propagation pulse reaction reaction-diffusion equations reaction-diffusion systems regeneration region Rinzel SD wave solitary wave soliton space spatial stability stochastic structures symmetric theorem theory thermodynamic tissue transform transition unstable values variable velocity wing disc Zabusky