30 research outputs found
Bifurcations in Globally Coupled Map Lattices
The dynamics of globally coupled map lattices can be described in terms of a
nonlinear Frobenius--Perron equation in the limit of large system size. This
approach allows for an analytical computation of stationary states and their
stability. The complete bifurcation behaviour of coupled tent maps near the
chaotic band merging point is presented. Furthermore the time independent
states of coupled logistic equations are analyzed. The bifurcation diagram of
the uncoupled map carries over to the map lattice. The analytical results are
supplemented with numerical simulations.Comment: 19 pages, .dvi and postscrip
Mixed problem for partial differential equations with quasihomogeneous principal part
This book offers the first systematic presentation of the theory of the mixed problem for hyperbolic differential equations with variable coefficients. This class includes hyperbolic and parabolic equations as well as nonclassic type of operator--the q-hyperbolic equation--which was introduced by the authors. As part of the exposition, the authors consider the Cauchy problem for this class of equations. This book would be suitable as a graduate textbook for courses in partial differential equations