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Compensation and stability in nonlinear matrix models

Authors
Journal
Mathematical Biosciences
0025-5564
Publisher
Elsevier
Publication Date
Volume
110
Issue
1
Identifiers
DOI: 10.1016/0025-5564(92)90015-o

Abstract

Abstract Stability, bifurcation, and dynamic behavior, investigated here in discrete, nonlinear, age-structured models, can be complex; however, restrictions imposed by compensatory mechanisms can limit the behavioral spectrum of a dynamic system. These limitations in transitional behavior of compensatory models are a focal point of this article. Although there is a tendency for compensatory models to be stable, we demonstrate that stability in compensatory systems does not always occur; for example, equilibria arising through a bifurcation can be initially unstable. Results concerning existence and uniqueness of equilibria, stability of the equilibria, and boundedness of solutions suggest that “compensatory” systems might not be compensatory in the literal sense.

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