Bifurcation and Chaos: Analysis, Algorithms, Applications

ISBN-13: 9783034870061 / Angielski / Miękka / 2012 / 388 str.

Kupper;Schneider;Seydel

Opis

This volume contains the proceedings of a conference held in Wiirzburg, August 20-24, 1990. The theme of the conference was Bifurcation and Chaos: Analysis, Algorithms, Ap plications. More than 100 scientists from 21 countries presented 80 contributions. Many of the results of the conference are described in the 49 refereed papers that follow. The conference was sponsored by the Deutsche Forschungsgemeinschaft, and by the Deutscher Akademischer Austauschdienst. We gratefully acknowledge the support from these agen cies. The science of nonlinear phenomena is evolving rapidly. Over the last 10 years, the emphasis has been gradually shifting. How trends vary may be seen by comparing these proceedings with previous ones, in particular with the conference held in Dortmund 1986 (proceedings published in ISNM 79). Concerning the range of phenomena, chaos has joined the bifurcation scenarios. As expected, the acceptance of chaos is less emotional among professionals, than it has been in some popular publications. A nalytical methods appear to have reached a state in which basic results of singularities, symmetry groups, or normal forms are everyday experience rather than exciting news. Similarly, numerical algorithms for frequent situations are now well established. Implemented in several packages, such algorithms have become standard means for attacking nonlinear problems. The sophisti cation that analytical and numerical methods have reached supports the vigorous trend to more and more applications. Pioneering equations as those named after Duffing, Van der Pol, or Lorenz, are no longer exclusively the state of art."

Spis treści

A Complete Bifurcation Scenario for the 2-d Nonlinear Laplacian with Neumann Boundary Conditions on the Unit Square.- The Effect of Fluctuations on the Transition Behavior of a Nonlinear Chemical Oscillator.- Examples of Boundary Crisis Phenomenon in Structural Dynamics.- Bifurcation, Pattern Formation and Transition to Chaos in Combustion.- On the Primary and Secondary Bifurcation of Equations Involving Scalar Nonlinearities.- Periodic Solutions Leading to Chaos in an Oscillator with Quadratic and Cubic Nonlinearities.- Turing Structures in Anisotropic Media.- Regular and Chaotic Patterns of Rayleigh-Bénard Convection.- Bifurcations in Slowly Rotating Systems with Spherical Geometry.- An Elastic Model with Continuous Spectrum.- Mechanistic Requirements for Chemical Oscillations.- Envelope Soliton Chans Model for Mechanical System.- Rolling Motion of Ships Treated as Bifurcation Problem.- Normal Forms for Planar Systems with Nilpotent Linear Part.- Two Methods for the Numerical Detection of Hopf Bifurcations.- Automatic Evaluation of First and Higher-Derivative Vectors.- On the Stability of a Spinning Satellite in a Central Force Field.- Codimension Two Bifurcation in an Approximate Model for Delayed Robot Control.- Lacunary Bifurcation of Multiple Solutions of Nonlinear Eigenvalue Problems.- Branches of Stationary Solutions for Parameter-dependent Reaction-Diffusion Systems from Climate Modeling.- A Note on the Detection of Chaos in Medium Sized Time Series.- An Approach for the Analysis of Spatially Localized Oscillations.- On the Application of Invariant Manifold Theory, in particular to Numerical Analysis.- Combined Analytical-Numerical Analysis of Nonlinear Dynamical Systems.- Monotony Methods and Minimal and Maximal Solutions for Nonlinear Ordinary Differential Equations.- Interior Crisis in an Electrochemical System.- Multiple Bifurcation of Free-Convection Flow Between Vertical Parallel Plates.- Description of Chaotic Motion by an Invariant Distribution at the Example of the Driven Duffing Oscillator.- Augmented Systems for Generalized Turning Points.- Numerical Analysis of the Orientability of Homoclinic Trajectories.- Qualitative and Quantitative Behaviour of Nonlinearly Elastic Rings under Hydrostatic Pressure.- Computation of Basins of Attraction for Three Coexisting Attractors.- Controllability of Lorenz Equation.- Spatially Periodic Forcing of Spatially Periodic Oscillators.- Solution Branches at Corank-Two Bifurcation Points with Symmetry.- Two-dimensional Maps Modelling Periodically Driven Strictly Dissipative Oscillators.- On Computing Coupled Turning Points of Parameter-Dependent Nonlinear Equations.- Generating Hopf Bifurcation Formulae with MAPLE.- On a Codimension Three Bifurcation Arising in an Autonomous Electronic Circuit.- Efficient Parallel Computation of Periodic Solutions of Parabolic Partial Differential Equations.- Comparison of Bifurcation Sets of Driven Strictly Dissipative Oscillators.- Echo Waves in Reaction-Diffusion Excitable Systems.- The Local Stability of Inactive Modes in Chaotic Multi-Degree-of-Freedom Systems.- Bifurcations in Dynamic Systems with Dry Friction.- The Approximate Analytical Methods in the Study of Bifurcations and Chaos in Nonlinear Oscillators.- Periodic and Homoclinic Orbits in Conservative and Reversible Systems.- On the Dynamics of a Horizontal, Rotating, Curved Shaft.- Lyapunov Exponents and Invariant Measures of Dynamic Systems.- Computation of Hopf Branches Bifurcating from Takens-Bogdanov Points for Problems with Symmetries.