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A computer-assisted study of global dynamic transitions for a noninvertible system. (English) Zbl 1185.37174

Summary: We present a computer-assisted analysis of the phase space features and bifurcations of a noninvertible, discrete-time system. Our focus is on the role played by noninvertibility in generating disconnected basins of attraction and the breakup of invariant circle solutions. Transitions between basin of attraction structures are identified and organized according to “levels of complexity”, a term we define in this paper. In particular, we present an algorithm that provides a computational approximation to the boundary (in phase space) separating points with different preimage behavior. The interplay between this boundary and other phase space features is shown to be crucial in understanding global bifurcations and transitions in the structure of the basin of attraction.

MSC:

37M99 Approximation methods and numerical treatment of dynamical systems
37-04 Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory
37E99 Low-dimensional dynamical systems
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