The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is comp...The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is computed by the fixed arclength method and the hyperbolic equilibrium is a saddle. The two-dimensional stable structure of Lorentz manifold is significant in people’s usual view. We also introduce the V-function to compute the V-manifold correspondingly. The defined V-function is smooth in the unstable direction of the manifold. Especially, the routh to period-doubling attractor on manifold surface is discussed too.展开更多
In this paper,we establish the existence of local stable manifolds for a semi-linear differential equation,where the linear part is a Hille-Yosida operator on a Banach space and the nonlinear forcing term f satisfies ...In this paper,we establish the existence of local stable manifolds for a semi-linear differential equation,where the linear part is a Hille-Yosida operator on a Banach space and the nonlinear forcing term f satisfies the ψ-Lipschitz conditions,where ψ belongs to certain classes of admissible function spaces.The approach being used is the fixed point arguments and the characterization of the exponential dichotomy of evolution equations in admissible spaces of functions defined on the positive half-line.展开更多
We construct stable invariant manifolds for semiflows generated by the nonlinear impulsive differential equation with parameters x'= A(t)x + f(t, x, λ), t≠τi and x(τ+i) = Bix(τi) + gi(x(τi), λ),...We construct stable invariant manifolds for semiflows generated by the nonlinear impulsive differential equation with parameters x'= A(t)x + f(t, x, λ), t≠τi and x(τ+i) = Bix(τi) + gi(x(τi), λ), i ∈ N in Banach spaces, assuming that the linear impulsive differential equation x'= A(t)x, t≠τi and x(τ+i) = Bix(τi), i ∈ N admits a nonuniform (μ, ν)-dichotomy. It is shown that the stable invariant manifolds are Lipschitz continuous in the parameter λ and the initial values provided that the nonlinear perturbations f, g are sufficiently small Lipschitz perturbations.展开更多
OGY method is the most important method of controlling chaos. It stabilizes a hyperbolic periodic orbit by making small perturbations for a system parameter. This paper improves the method of choosing parameter, and g...OGY method is the most important method of controlling chaos. It stabilizes a hyperbolic periodic orbit by making small perturbations for a system parameter. This paper improves the method of choosing parameter, and gives a mathematics proof of it.展开更多
A class of large scale geophysical fluid flows are modelled by the quasi-geostrophic equation. An averaging principle for quasi-geostrophic motion under rapidly oscil-lating ( non-autonomous) forcing was obtained, bot...A class of large scale geophysical fluid flows are modelled by the quasi-geostrophic equation. An averaging principle for quasi-geostrophic motion under rapidly oscil-lating ( non-autonomous) forcing was obtained, both on finite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and convergence result between quasi-geostrophic motions and its averaged motions. Furthermore, the existence of almost periodic quasi-geostrophic motions and attractor convergence were also investigated.展开更多
Transient angle stability of inverters equipped with the robust droop controller is investigated in this work.At first,the conditions on the control references to guarantee the existence of a feasible post-disturbance...Transient angle stability of inverters equipped with the robust droop controller is investigated in this work.At first,the conditions on the control references to guarantee the existence of a feasible post-disturbance operating point are derived.Then,the post-disturbance equilibrium points are found and their stability properties are characterized.Furthermore,the attraction regions of the stable equilibrium points are accurately depicted by calculating the stable and unstable manifolds of the surrounding unstable equilibrium points,which presents an explanation to system transient stability.Finally,the transient control considerations are provided to help the inverter ridethrough the disturbance and maintain its stability characteristics.It is shown that the transient angle stability is not a serious problem for droop controlled inverters with proper control settings.展开更多
Under a generic assumption, the existence and the uniqueness of the periodic orbit generating from a homoclinic bifurcation are shown, and the dimensions of its stable and unstable manifolds are given. In the case of ...Under a generic assumption, the existence and the uniqueness of the periodic orbit generating from a homoclinic bifurcation are shown, and the dimensions of its stable and unstable manifolds are given. In the case of a 3-dimensional system, our result revises the stability criterion given in [4,5].展开更多
文摘The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is computed by the fixed arclength method and the hyperbolic equilibrium is a saddle. The two-dimensional stable structure of Lorentz manifold is significant in people’s usual view. We also introduce the V-function to compute the V-manifold correspondingly. The defined V-function is smooth in the unstable direction of the manifold. Especially, the routh to period-doubling attractor on manifold surface is discussed too.
基金Deanship of Scientific Research at Majmaah University for supporting this work under Project Number No.R-1441-27.
文摘In this paper,we establish the existence of local stable manifolds for a semi-linear differential equation,where the linear part is a Hille-Yosida operator on a Banach space and the nonlinear forcing term f satisfies the ψ-Lipschitz conditions,where ψ belongs to certain classes of admissible function spaces.The approach being used is the fixed point arguments and the characterization of the exponential dichotomy of evolution equations in admissible spaces of functions defined on the positive half-line.
基金supported by National Natural Science Foundation of China(Grant Nos.11126269 and 11201128)supported by National Natural Science Foundation of China(Grant Nos.10971022 and 11271065)
文摘We construct stable invariant manifolds for semiflows generated by the nonlinear impulsive differential equation with parameters x'= A(t)x + f(t, x, λ), t≠τi and x(τ+i) = Bix(τi) + gi(x(τi), λ), i ∈ N in Banach spaces, assuming that the linear impulsive differential equation x'= A(t)x, t≠τi and x(τ+i) = Bix(τi), i ∈ N admits a nonuniform (μ, ν)-dichotomy. It is shown that the stable invariant manifolds are Lipschitz continuous in the parameter λ and the initial values provided that the nonlinear perturbations f, g are sufficiently small Lipschitz perturbations.
文摘OGY method is the most important method of controlling chaos. It stabilizes a hyperbolic periodic orbit by making small perturbations for a system parameter. This paper improves the method of choosing parameter, and gives a mathematics proof of it.
文摘A class of large scale geophysical fluid flows are modelled by the quasi-geostrophic equation. An averaging principle for quasi-geostrophic motion under rapidly oscil-lating ( non-autonomous) forcing was obtained, both on finite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and convergence result between quasi-geostrophic motions and its averaged motions. Furthermore, the existence of almost periodic quasi-geostrophic motions and attractor convergence were also investigated.
基金supported in part by National Natural Science Foundation of China (No.51877133)China Scholarship Council,and National Science Foundation (Award No.1810105)。
文摘Transient angle stability of inverters equipped with the robust droop controller is investigated in this work.At first,the conditions on the control references to guarantee the existence of a feasible post-disturbance operating point are derived.Then,the post-disturbance equilibrium points are found and their stability properties are characterized.Furthermore,the attraction regions of the stable equilibrium points are accurately depicted by calculating the stable and unstable manifolds of the surrounding unstable equilibrium points,which presents an explanation to system transient stability.Finally,the transient control considerations are provided to help the inverter ridethrough the disturbance and maintain its stability characteristics.It is shown that the transient angle stability is not a serious problem for droop controlled inverters with proper control settings.
基金Supported by the National Natural Science Foundation of China
文摘Under a generic assumption, the existence and the uniqueness of the periodic orbit generating from a homoclinic bifurcation are shown, and the dimensions of its stable and unstable manifolds are given. In the case of a 3-dimensional system, our result revises the stability criterion given in [4,5].