Bifurcation and Chaos: Analysis, Algorithms, Applications

Abstract

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-Benard 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.