Suppression of explosion by polynomial noise for nonlinear differential systems

  • Lichao Feng
  • Shoumei Li
  • Renming Song
  • Yemo Li
Research Paper


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)| ß Ax(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.


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



This work was partially supported by National Natural Science Foundation of China (Grant No. 11571024), China Postdoctoral Science Foundation (Grant No. 2017M621588), Natural Science Foundation of Hebei Province of China (Grant No. A2015209229), Science and Technology Research Foundation of Higher Education Institutions of Hebei Province of China (Grant No. QN2017116), Grant From the Simons Foundation (Grant No. 429343, Renming Song), and Graduate Foundation of the North China University of Science and Technology (Grant No. K1603).


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Lichao Feng
    • 1
    • 2
    • 3
  • Shoumei Li
    • 2
  • Renming Song
    • 4
    • 2
  • Yemo Li
    • 1
  1. 1.College of ScienceNorth China University of Science and TechnologyTangshanChina
  2. 2.College of Applied SciencesBeijing University of TechnologyBeijingChina
  3. 3.School of Mathematics, and Research Center for Complex Systems and Network SciencesSoutheast UniversityNanjingChina
  4. 4.Department of MathematicsUniversity of IllinoisUrbanaUSA

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