期刊
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
卷 14, 期 1, 页码 53-82出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2012.05.002
关键词
Bifurcation; Global continuation; Periodic difference equation; Floquet spectrum; Population dynamics
This paper investigates local and global bifurcation, as well as continuation properties for discrete-time periodic dynamical models in arbitrary (finite) dimension. Our focus is to provide explicitly verifiable conditions which guarantee or prevent bifurcations of, say NI-periodic solutions for No-periodic difference equations. In doing so, we give concrete branching relations ensuring bifurcations of e.g. fold, transcritical, pitchfork or flip type, including information on the global branches. Beyond that we obtain formulas indicating the local behavior of mean population sizes under parameter variation or bifurcation, and furthermore tackle stability issues. Our results are applied to various real-world population models. Thus, the paper will be useful for a thorough analysis and understanding of general periodic time-discrete models in population dynamics, life sciences and beyond. (C) 2012 Elsevier Ltd. All rights reserved.
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