Bifurcation and Chaos: Analysis, Algorithms, Applications

Front Matter....Pages I-X
A Complete Bifurcation Scenario for the 2-d Nonlinear Laplacian with Neumann Boundary Conditions on the Unit Square....Pages 1-18
The Effect of Fluctuations on the Transition Behavior of a Nonlinear Chemical Oscillator....Pages 19-25
Examples of Boundary Crisis Phenomenon in Structural Dynamics....Pages 27-36
Bifurcation, Pattern Formation, and Transition to Chaos in Combustion....Pages 37-52
On the Primary and Secondary Bifurcation of Equations Involving Scalar Nonlinearities....Pages 53-57
Periodic Solutions Leading to Chaos in an Oscillator with Quadratic and Cubic Nonlinearities....Pages 59-65
Turing Structures in Anisotropic Media....Pages 67-77
Regular and Chaotic Patterns of Rayleigh-Benard Convection....Pages 79-92
Bifurcations in slowly rotating systems with spherical geometry....Pages 93-97
An Elastic Model with Continuous Spectrum....Pages 99-103
Mechanistic Requirements for Chemical Oscillations....Pages 105-109
Envelope Soliton Chaos Model for Mechanical System....Pages 111-115
Rolling Motion of Ships Treated as Bifurcation Problem....Pages 117-121
Normal Forms for Planar Systems With Nilpotent Linear Part....Pages 123-127
Two Methods for the Numerical Detection of Hopf Bifurcations....Pages 129-133
Automatic Evaluation of First and Higher-Derivative Vectors....Pages 135-148
On the Stability of a Spinning Satellite in a Central Force Field....Pages 149-153
Codimension Two Bifurcation in an Approximate Model for Delayed Robot Control....Pages 155-159
Lacunary Bifurcation of Multiple Solutions of Nonlinear Eigenvalue Problems....Pages 161-169
Branches of Stationary Solutions for Parameter-dependent Reaction-Diffusion Systems from Climate Modeling....Pages 171-175
A Note on the Detection of Chaos in Medium Sized Time Series....Pages 177-181
An approach for the analysis of spacially localized oscillations....Pages 183-187
On the Application of Invariant Manifold Theory, in particular to Numerical Analysis....Pages 189-197
Combined Analytical — Numerical Analysis of Nonlinear Dynamical Systems....Pages 199-203
Monotony methods and minimal and maximal solutions for nonlinear ordinary differential equations....Pages 205-209
Interior Crisis in an Electrochemical System....Pages 211-215
Multiple Bifurcation of Free-Convection Flow between Vertical Parallel Plates....Pages 217-223
Description of Chaotic Motion by an Invariant Distribution at the Example of the Driven Duffing Oszillator....Pages 225-230
Augmented Systems for Generalized Turning Points....Pages 231-236
Numerical Analysis of the Orientability of Homoclinic Trajectories....Pages 237-242
Qualitative and Quantitative Behaviour of Nonlinearly Elastic Rings under Hydrostatic Pressure....Pages 243-247
Computation of Basins of Attraction for Three Coexisting Attractors....Pages 249-255
Controllability of Lorenz Equation....Pages 257-261
Spatially Periodic Forcing of Spatially Periodic Oscillators....Pages 263-275
Solution Branches at Corank-2 Bifurcation Points with Symmetry....Pages 277-281
Two-dimensional maps modelling periodically driven strictly dissipative oscillators....Pages 283-287
On Computing Coupled Turning Points of Parameter Dependent Nonlinear Equations....Pages 289-294
Generating Hopf Bifurcation Formulae with MAPLE....Pages 295-299
On a Codimension 3 Bifurcation Arising in an Autonomous Electronic Circuit....Pages 301-306
Efficient Parallel Computation of Periodic Solutions of Parabolic Partial Differential Equations....Pages 307-317
Comparison of bifurcation sets of driven strictly dissipative oscillators....Pages 319-323
Echo Waves in Reaction-Diffusion Excitable Systems....Pages 325-331
The Local Stability of Inactive Modes in Chaotic Multi-Degree-of-Freedom Systems....Pages 333-342
Bifurcations in Dynamic Systems with Dry Friction....Pages 343-347
The Approximate Analytical Methods in the Study of Bifurcations and Chaos in Nonlinear Oscillators....Pages 349-353
Periodic and homoclinic orbits in conservative and reversible systems....Pages 355-359
On the Dynamics of a Horizontal, Rotating, Curved Shaft....Pages 361-365
Lyapunov Exponents and Invariant Measures of Dynamic Systems....Pages 367-376
Computation of Hopf Branches Bifurcating from Takens-Bogdanov Points for Problems with Symmetries....Pages 377-388