By Hal L. Smith
This booklet offers the 1st entire remedy of a quickly constructing region with many strength functions: the idea of monotone dynamical platforms and the speculation of aggressive and cooperative differential equations. the first goal is to supply power clients of the idea with concepts, effects, and ideas necessary in functions, whereas while delivering rigorous proofs. the most results of the 1st chapters, which deal with continuous-time monotone dynamical structures, is that the regularly occurring orbit converges to an equilibrium. the following chapters care for independent, aggressive and cooperative, usual differential equations: each answer within the airplane has finally monotone elements, and the Poincare-Bendixson conception in 3 dimensions is mentioned. chapters study quasimonotone and nonquasimonotone hold up differential equations, and the publication closes with a dialogue of purposes to quasimonotone platforms of reaction-diffusion kind. all through, Smith discusses functions of the speculation to many mathematical versions coming up in biology. an in depth advisor to the literature is supplied on the finish of every bankruptcy. Requiring a history in dynamical platforms on the point of a primary graduate direction, this e-book will be compatible as a graduate textual content for a themes direction.