اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدStochastic Bifurcation of Pathwise Random Almost Periodic and Almost Automorphic Solutions for Random Dynamical Systems
239
0
0.0
(
0
)
تأليف
Bixiang Wang
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper, we introduce concepts of pathwise random almost periodic and almost automorphic solutions for dynamical systems generated by non-autonomous stochastic equations. These solutions are pathwise stochastic analogues of deterministic dynamical systems. The existence and bifurcation of random periodic (random almost periodic, random almost automorphic) solutions have been established for a one-dimensional stochastic equation with multiplicative noise.
قيم البحث
اقرأ أيضاً
The paper is dedicated to studying the problem of Poisson stability (in particular stationarity, periodicity, quasi-periodicity, Bohr almost periodicity, Bohr almost automorphy, Birkhoff recurrence, almost recurrence in the sense of Bebutov, Levitan
almost periodicity, pseudo-periodicity, pseudo-recurrence, Poisson stability) of solutions for semi-linear stochastic equation $$ dx(t)=(Ax(t)+f(t,x(t)))dt +g(t,x(t))dW(t)quad (*) $$ with exponentially stable linear operator $A$ and Poisson stable in time coefficients $f$ and $g$. We prove that if the functions $f$ and $g$ are appropriately small, then equation $(*)$ admits at least one solution which has the same character of recurrence as the functions $f$ and $g$.
In this paper, we use the variational approach to investigate recurrent properties of solutions for stochastic partial differential equations, which is in contrast to the previous semigroup framework. Consider stochastic differential equations with m
onotone coefficients. Firstly, we establish the continuous dependence on initial values and coefficients for solutions. Secondly, we prove the existence of recurrent solutions, which include periodic, almost periodic and almost automorphic solutions. Then we show that these recurrent solutions are globally asymptotically stable in square-mean sense. Finally, for illustration of our results we give two applications, i.e. stochastic reaction diffusion equations and stochastic porous media equations.
The concept of square-mean almost automorphy for stochastic processes is introduced. The existence and uniqueness of square-mean almost automorphic solutions to some linear and non-linear stochastic differential equations are established provided the
coefficients satisfy some conditions. The asymptotic stability of the unique square-mean almost automorphic solution in square-mean sense is discussed.
In this paper, we discuss the relationships between stability and almost periodicity for solutions of stochastic differential equations. Our essential idea is to get stability of solutions or systems by some inherited properties of Lyapunov functions
. Under suitable conditions besides Lyapunov functions, we obtain the existence of almost periodic solutions in distribution.
By the Lyapunov-Perron method,we prove the existence of random inertial manifolds for a class of equations driven simultaneously by non-autonomous deterministic and stochastic forcing. These invariant manifolds contain tempered pullback random attrac
tors if such attractors exist. We also prove pathwise periodicity and almost periodicity of inertial manifolds when non-autonomous deterministic forcing is periodic and almost periodic in time, respectively.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
