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A Mechanism For Stabilization of Dynamics in Nonlinear Systems with Different Time Scales

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 characteristics stabilize. We analyze certain one-dimensional and two-dimensional nonlinear systems, and try to generalize our results to higher dimensions.

Article Number:
MTBI-05-01M

Year:
2008

Authors:
Raquel M. Lopez, Arizona State University
Erika T. Camacho, Arizona State University-West
Sergei K. Suslov, Arizona State University

a_mechanism_for_stabilization_of_dynamics_in_nonlinear_systems_with_different_time_scales_.pdf