Bifurcation: Analysis, Algorithms, Applications

The conference on BIFURCATIONS: ANALYSIS, ALGORITHMS, APPLICATIONS took place in Dortmund in August 18 - 22, 1986. More then 150 Scientists from 16 countries participated in the meeting, among them mathematicians, engi­ neers, and physicists. A broad spectrum of new results on bifurcation was covered by 49 talks. The diversity of the range of treated topics and of involved fields inspired fruitful discussions. 36 refereed papers are contained in these proceedings. The subjects covered treat bifurcation problems, ranging from theoretical investigations to numerical results, with emphasis placed upon applications. The more theoreti­ cal papers include the topics symmetry breaking, delay differential equations, Cornu spirals, homoclinic orbits, and selfsimilarity. Different kinds of bifurcations are treated: Hopf bifurcation, bifurcation from continuous spec­ trum, complex bifurcation, and bifurcation near tori. Several numerical as­ pects are discussed, among them continuation, block elimination, and spectral methods. Algorithms are proposed for approximating manifolds, calculating pe­ riodic solutions and handling multi-parameter problems. Ample space is devoted to· applications. Classical phenomena from fluid mechanics (such as convection rolls and th~ Taylor vortex problem), buckling, and reaction-diffusion pro­ blems are considered. Other applications of bifurcations include railway vehicle dynamics, computer graphics, semiconductors, drilling processes, simu­ lation of oil reservoirs, and rotor dynamics. The proceedings reflect current research in bifurcation. They are an attempt to bring together researchers from differ~nt disciplines to stimulate common effort towards a better understanding and handling of bifurcation pro­ blems.

The effect of discretization on homoclinic orbits.- Bifurcation in elliptic systems.- Transition to asymmetric convection rolls.- Wave patterns in coupled stationary bifurcations with 0(2)-symmetry.- Determination of bifurcation points and catastrophes for the Brusselator model with two parameters.- Numerical studies of bifurcation in reactiondiffusion models using pseudo-spectral and path-following methods.- A quick multiparameter test for periodic solutions.- Codimension two bifurcations near an invariant n-torus.- Hopf bifurcation in the drilling process under regenerative cutting conditions.- Critical points of mixed fluids and their numerical treatment.- Bifurcation theory in physics: Recent trends and problems.- An application of complex bifurcation to a problem in computer graphics.- Continuation of periodic solutions in parabolic partial differential equations.- Bifurcation in degenerate directions.- On Cornu spirals. Disorder, selfsimilarity, and Jacobi s ?3(?, ?).- Optimization in bifurcation problems using a continuation method.- On the numerical study of bifurcation problems.- External forcing in a glycolytic model.- Some remarks on the morphology of non-unique solutions in nonlinear elastostatics.- Lusternik-SGhnirelmann critical values and bifurcation problems.- Adaptive numerical Lyapunov-Schmidt-reduction.- Formation of periodic and aperiodic waves in reaction-diffusion systems.- Steady axisymmetric Taylor vortex flows with free stagnation points of the poloidal flow.- Some remarks on the deflated block elimination method.- Nonlinear dynamic behavior and buckling of shells of revolution.- The curious link chain.- On a moving-frame algorithm and the triangulation of equilibrium manifolds.- Numerical computation of origins for Hopf bifurcation in atwo-parameter problem.- Bifurcations of the equilibrium of a spherical double pendulum at a multiple eigenvalue.- Multiple solutions of the semiconductor equations.- Delay as bifurcation parameter.- Bifurcation from the continuous spectrum in LP(?).- Bifurcation problems in railway vehicle dynamics.- Bifurcation and post-bifurcation behaviour for elastic-plastic solids.- Symmetry-breaking at positive solutions of elliptic equations.- Averaging over angles with an application to rótor dynamics.