TY - JOUR
T1 - Suppression of explosion by polynomial noise for nonlinear differential systems
AU - Feng, Lichao
AU - Li, Shoumei
AU - Song, Renming
AU - Li, Yemo
N1 - Funding Information:
Acknowledgements 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).
PY - 2018/7/1
Y1 - 2018/7/1
N2 - 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.
AB - 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.
KW - decay with general rate
KW - explosion suppression
KW - general polynomial growth condition
KW - growth with general rate
KW - noise
KW - non-autonomous differential system
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U2 - 10.1007/s11432-017-9340-4
DO - 10.1007/s11432-017-9340-4
M3 - Article
AN - SCOPUS:85048325787
VL - 61
JO - Science China Information Sciences
JF - Science China Information Sciences
SN - 1674-733X
IS - 7
M1 - 70215
ER -