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