Suppression of explosion by polynomial noise for nonlinear differential systems

Lichao Feng, Shoumei Li, Renming Song, Yemo Li

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study the problem of the suppression of explosion by noise for nonlinear non-autonomous differential systems. For a deterministic non-autonomous differential system dx(t) = f(x(t), t)dt, which can explode at a finite time, we introduce polynomial noise and study the perturbed system dx(t) = f(x(t), t)dt + h(t) 12 |x(t)|ßAx(t)dB(t). We demonstrate that the polynomial noise can not only guarantee the existence and uniqueness of the global solution for the perturbed system, but can also make almost every path of the global solution grow at most with a certain general rate and even decay with a certain general rate (including super-exponential, exponential, and polynomial rates) under specific weak conditions.

Original languageEnglish (US)
Article number70215
JournalScience China Information Sciences
Volume61
Issue number7
DOIs
StatePublished - Jul 1 2018

Keywords

  • decay with general rate
  • explosion suppression
  • general polynomial growth condition
  • growth with general rate
  • noise
  • non-autonomous differential system

ASJC Scopus subject areas

  • Computer Science(all)

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