Nonlinear Nonautonomous Difference Equations
Global Behavior and Applications
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Beschreibung
The De Gruyter Series in Mathematics and Life Sciences is devoted to the publication of monographs in the field. They cover topics and methods in fields of current interest that use mathematical approaches to understand and explain, model and influence phenomena in all areas of life sciences. This includes, among others, theory and application of biological mathematical modeling, complex systems biology, bioinformatics, computational biomodeling stochastic modeling, biostatistics, computational evolutionary biology, comparative genomics, or structural bioinformatics. Also, new types of mathematical problems that arise from biological knowledge shall be covered.
The aim of this monograph is to initiate and facilitate a systematic study of the global asymptotic behavior of nonlinear nonautonomous difference equations. In addition to general classes of nonautonomous equations, a focus lies on some special classes including periodic and asymptotically autonomous equations. The authors' primary goal is to study global stability, in particular the extreme stability (path stability), as well as the global asymptotic stability in periodic equations. In addition, they explore the oscillatory character of solutions including semicycles analysis, boundednes and persistence, permanence, the existence and the character of solutions having special properties such as periodicity, unboundedness, or monotonicity. Special attention is placed on the notion of attenuance and resonance of periodic cycles and their generalizations. This monograph presents to the reader a broad spectrum of approaches to the mentioned problems and contains several important developments in this area with applications mainly to Mathematical Biology as well as to other disciplines. In the Appendix some issues about the dynamics of discontinuous population models and discontinuous difference equations are addressed. The reader is exposed to the frontiers of the discipline, including a variety of important open problems and conjectures that require immediate attention.
Autor*in
Vlajko L. Kocic
Themen in »Nonlinear Nonautonomous Difference Equations«
Dynamisches System Nichtlineare Differenzengleichung Nichtautonomes System