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Singular fold with real noise

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


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