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Uniqueness of limit cycles for a class of cubic system with an invariant straight line
Abstract A class of cubic system with an invariant straight line as given in an equation is studied. It is proved that this system has at most, one limit cycle surrounding a weak focal O ( 0 , 0 ) ,Expand
Mean-square numerical approximations to random periodic solutions of stochastic differential equations
This paper is devoted to the possibility of mean-square numerical approximations to random periodic solutions of dissipative stochastic differential equations. The existence and expression of randomExpand
Shadowing orbits of a class of random differential equations
Abstract This article focuses on the existence of a true solution near a numerical approximate solution of random differential equations which can generate random dynamical systems. We prove aExpand
Stochastic shadowing analysis of a class of stochastic differential equations
This paper is devoted to the feasibility of stochastic shadowing of a class of stochastic differential equations via numerical analysis tools. A general shadowing theorem of stochastic differentialExpand
Numerical study on (ω, Lδ)-Lipschitz shadowing of stochastic differential equations
TLDR
A new notion of random Lipschitz shadowing and exact estimation of shadowing distance of stochastic differential equations are investigated and the measurability of the true orbits is studied. Expand
Stability Results for a Class of Differential Equation and Application in Medicine
A Chemostat system incorporating hepatocellular carcinomas is discussed. The model generalizes the classical Chemostat model, and it assumes that the Chemostat is an increasing function of theExpand
Numerical Study on Stochastic Diabetes Mellitus Model with Additive Noise
TLDR
The existence and uniqueness theorem of the solution under some appropriate assumptions is established and the mean square stability and convergence of numerical solutions are proposed, too. Expand
Symplectic Euler scheme for Hamiltonian stochastic differential equations driven by Levy noise
TLDR
A general symplectic Euler scheme for a class of Hamiltonian stochastic differential equations driven by L$\acute{e}$vy noise in the sense of Marcus form is proposed. Expand
Dynamical analysis in explicit continuous iteration algorithm and its applications
This article is devoted to the dynamical analysis of an explicit continuous iteration algorithm, describing its construction, relationship with the explicit trapezoid method, and error analysis. AExpand
Hopf bifurcation and uniqueness of limit cycle for a class of quartic system
AbstractThis paper studies a class of quartic system which is more general and realistic than the quartic accompanying system. * $$x' = - y + ex + lx^2 + mxy + ny^2 , y' = x(1 - Ay)(1 + Cy^2 ),$$ Expand
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