Singular fold with real noise

Peter W. Bates; Ji  Li; Mingji  Zhang

doi:10.3934/dcdsb.2016038

Article Contents

2016, Volume 21, Issue 7: 2091-2107. Doi: 10.3934/dcdsb.2016038

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Singular fold with real noise

1.
Department of Mathematics, Michigan State University, East Lansing, MI 48824
2.
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074
3.
Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801

Received: November 2015

Revised: January 2016

Published: September 2016

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Abstract

We study the effect of small real noise on the jump behavior near a singular fold point, which is an important step in understanding the burst-spike behavior in many biological models. We show by the theory of center manifolds and random invariant manifolds that if the order of the noise is high enough, trajectories essentially pass the fold point in the manner as though there is no noise.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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