A Mechanism for Stabilization of Dynamics in Nonlinear Systems with Different Time Scales
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ID: 282125
2009
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Abstract
There are many natural, physical, and biological systems that exhibit
multiple time scales. For example, the dynamics of a population of ticks can be
described in continuous time during their individual life cycle yet discrete
time is used to describe the generation of offspring. These characteristics
cause the population levels to be reset periodically. A similar phenomenon can
be observed in a sociological college drinking model in which the population is
reset by the incoming class each year, as described in the 2006 work of Camacho
et al. With the latter as our motivation we analytically and numerically
investigate the mechanism by which solutions in certain systems with this
resetting conditions stabilize. We further utilize the sociological college
drinking model as an analogue to analyze certain one-dimensional and
two-dimensional nonlinear systems, as we attempt to generalize our results to
higher dimensions.
| Reference Key |
camacho2009a
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|---|---|
| Authors | Raquel M. Lopez; Sergei K. Suslov; Erika T. Camacho |
| Journal | arXiv |
| Year | 2009 |
| DOI |
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