Global Asymptotic Behavior Research Articles

Global asymptotic behavior for mixed vaccination strategy in a delayed epidemic model with interim-immune.

Vaccination strategy is considered as the most cost-effective intervention measure for controlling diseases. It will strengthen the immunity and reduce the risks of infections. In this paper, a new delayed epidemic model with interim-immune and mixed vaccination strategy is studied. The diseasefree periodic solution is obtained by twice stroboscopic mapping and the corresponding dynamical behavior is analyzed. We determine a threshold parameter R1, the disease-free periodic solution is proved to be global attractive if R1 < 1. We also establish a threshold parameter R2 for the permanence of the model, i.e., if R2 > 1, the infectious disease will exist persistently. Then, we provide numerical simulations to illustrate our theoretical results intuitively. In particular, a practical application for newtype TB vaccine under mixed vaccination strategy is presented, based on the proposed theory and the data reported by NBSC. The mixed vaccination strategy can achieve the End TB goal formulated by WHO in limited time. Our study will help public health agency to design mixed control strategy which can reduce the burden of infectious diseases.

一类具有对数非线性项的四阶抛物型方程解的全局渐近性

一类具有对数非线性项的四阶抛物型方程解的全局渐近性

Modeling the Effect of Fear in a Prey–Predator System with Prey Refuge and Gestation Delay

Recently, some field experiments and studies show that predators affect prey not only by direct killing, they induce fear in prey which reduces the reproduction rate of prey species. Considering this fact, we propose a mathematical model to study the fear effect and prey refuge in prey–predator system with gestation time delay. It is assumed that prey population grows logistically in the absence of predators and the interaction between prey and predator is followed by Crowley–Martin type functional response. We obtained the equilibrium points and studied the local and global asymptotic behaviors of nondelayed system around them. It is observed from our analysis that the fear effect in the prey induces Hopf-bifurcation in the system. It is concluded that the refuge of prey population under a threshold level is lucrative for both the species. Further, we incorporate gestation delay of the predator population in the model. Local and global asymptotic stabilities for delayed model are carried out. The existence of stable limit cycle via Hopf-bifurcation with respect to delay parameter is established. Chaotic oscillations are also observed and confirmed by drawing the bifurcation diagram and evaluating maximum Lyapunov exponent for large values of delay parameter.

Decay estimates for a dissipative-dispersive linear semigroup and application to the viscous Boussinesq equation

At the core of this article is the new estimate for a class of dissipative-dispersive linear semigroup eΔt±ip(|∇|)t arising in the study of the viscous Boussinesq equation. We combine the decay estimate with introducing a set of time-weighted Sobolev spaces, where the time-weights and the regularity of the Sobolev spaces are determined by our decay estimate, to show the global existence and asymptotic behavior of solutions to the viscous Boussinesq equation in Rn.

Global well-posedness and asymptotic behavior for the 2D Boussinesq system with variable viscosity

In this paper, we investigate the global existence and uniqueness of strong solutions to 2D Boussinesq system with variable kinematic viscosity depending on the temperature. Comparing with the previous results given by Abidi and Zhang [4] who considered the critical case α=1, we weaken the dissipation effect in the temperature equation to the supercritical case α∈(0,1). Furthermore, we obtain the algebraic decay estimate for ||u||L2.

Global existence, asymptotic behavior and uniform attractors for a non-autonomous Timoshenko system of thermoelasticity of type III with a time-varying delay

In this paper, we first establish the global existence by using the variable norm technique of Kato and semigroup method. Second, under suitable assumptions on the data, we obtain the asymptotic behavior of the solution. Last, we prove the existence of a uniform attractor by using the method of uniform contractive functions.

The Attractors of Camassa–Holm Equation in Unbounded Domains

In this paper, we deal with the existence of global mild solutions and asymptotic behavior to the viscous Camassa–Holm equation in the locally uniform spaces. First we establish the global well-posedness for the Cauchy problem of viscous Camassa–Holm equation in $${\mathbb {R}}^1$$ for any initial data $$u_0\in {\dot{H}}^1_U({\mathbb {R}}^1).$$ Then we study the long time dynamical behavior of non-autonomous viscous Camassa–Holm equation on $${\mathbb {R}}^1$$ with a new class of external forces and show the existence of $$(H^1_U({\mathbb {R}}^1),H^1_\phi ({\mathbb {R}}^1))$$ -uniform(w.r.t. $$g\in \mathcal {H}_{L^2_U({\mathbb {R}}^1)}(g_0)$$ ) attractor $$\mathcal {A}_{\mathcal {H}_{L^2_U({\mathbb {R}}^1)}(g_0)}$$ with locally uniform external forces being translation uniform bounded but not translation compact in $$L_b^2({\mathbb {R}};L^2_U({\mathbb {R}}^1))$$ .

Optimal global asymptotic behavior of the solution to a singular monge-ampère equation

This paper is mainly concerned with the optimal global asymptotic behavior of the unique convex solution to a singular Dirichlet problem for the Monge-Ampere equation \begin{document}$ {\rm det} D^2 u = b(x)g(-u), u where \begin{document}$ \Omega $\end{document} is a strict convex and bounded smooth domain in \begin{document}$ \mathbb R^n $\end{document} with \begin{document}$ n\geq 2 $\end{document} , \begin{document}$ g\in C^1((0,\infty)) $\end{document} is positive and decreasing in \begin{document}$ (0, \infty) $\end{document} with \begin{document}$ \lim_{s \rightarrow 0^+}g(s) = \infty $\end{document} , \begin{document}$ b \in C^{\infty}(\Omega) $\end{document} is positive in \begin{document}$ \Omega $\end{document} , but may vanish or blow up on the boundary properly. Our approach is based on the construction of suitable sub- and super-solutions.

Global Existence and Asymptotic Behavior of Solutions for Some Coupled Systems via a Lyapunov Functional

The purpose of this work is to study the global existence and asymptotic behavior of solutions to a coupled reaction-diffusion system describing epidemiological or chemical situations. Our analytical proofs are based on the Lyapunov functional methods.

Global existence and asymptotic behavior of classical solutions to a fractional logistic Keller–Segel system

In this paper we consider a fractional parabolic–elliptic Keller–Segel system with a logistic source on RN. First, we establish the regularity of weak solutions of the fractional parabolic equation, using blow-up arguments combined with Liouville-type theorems. Next, by the semigroup method and regularity results we prove the local existence and uniqueness of classical solutions. Moreover, the global existence and boundedness of classical solutions for given initial data are obtained under some conditions. Finally, we show the asymptotic behavior of the global solutions with strictly positive initial data.

Global well-posedness for a class of fourth-order nonlinear strongly damped wave equations

Abstract In this paper, we consider the initial boundary value problem for a class of fourth-order wave equations with strong damping term, nonlinear weak damping term, strain term and nonlinear source term in polynomial form. First, the local solution is obtained by using fix point theory. Then, by constructing the potential well structure frame, we get the global existence, asymptotic behavior and blowup of solutions for the subcritical initial energy and critical initial energy respectively. Ultimately, we prove the blowup in finite time of solutions for the arbitrarily positive initial energy case.

Global Behavior of a Discrete Anticompetitive System in the Plane

The main goal of this paper is to investigate the global asymptotic behavior of the difference systemxn+1=γ1yn/A1+xn, yn+1=β2xn/B2+yn, n=0,1,2,….withγ1,β2,A1,B2∈(0,∞)and the initial condition(x0,y0)∈[0,∞)×[0,∞). We obtain some global attractivity results of this system for different values of the parameters, which answer the open problem proposed in “Rational systems in the plane, J. Difference Equ. Appl. 15 (2009), 303-323”.

Global existence, boundedness and asymptotic behavior to a chemotaxis model with singular sensitivity and logistic source

ABSTRACT This article deals with the chemotaxis model with singular sensitivity and logistic source under homogenous Neumann boundary condition in a smooth bounded domain , with and for all s>0 with . For , we show that the system admits a global classical solution that provides , and . Furthermore, for N=2, under the assumptions above, we obtain the boundedness and asymptotic behavior of solutions that provide , , and μ sufficiently large.

The global solvability and asymptotic behavior of a transmission problem for Kirchhoff‐type wave equations with memory source on the boundary

A transmission problem for Kirchhoff‐type wave equations with memory source term on one part of the boundary feedback is considered. By using the Faedo‐Galerkin approximation technique, the method of Lyapunov functional and the energy perturbation technique, we establish well‐posedness of global solution and derive a general decay estimate of the energy.

Global existence and asymptotic behavior of the fractional chemotaxis system with signal-dependent sensitivity

In this paper, we study a fractional chemotaxis model with signal-dependent sensitivity and the source term, which involves two parabolic equations with fractional diffusions. We develop a suitable mathematical framework for a unified treatment of the existence and decay estimates. Based on an appropriate functional space, we show the existence, uniqueness and temporal decay of the global classical solutions to the problem simultaneously under the smallness initial assumptions.

Global existence, uniqueness, and asymptotic behavior of solution for the Euler-Bernoulli viscoelastic equation

Global existence, uniqueness, and asymptotic behavior of solution for the Euler-Bernoulli viscoelastic equation

Dynamics of prey–predator model with stage structure in prey including maturation and gestation delays

This study proposes a three-dimensional prey–predator model with stage structure in prey (immature and mature) including maturation delay in prey population and gestation delay in predator population. It is assumed that the immature prey population is consumed by predators with Holling type I functional response and the interaction between mature prey and predator species is followed by Crowley–Martin-type functional response. We analyzed the equilibrium points, local and global asymptotic behavior of interior equilibrium point for the non-delayed system. Hopf-bifurcation with respect to different parameters has also been studied for the system. Further, the existence of periodic solutions through Hopf-bifurcation is shown with respect to both the delays. Our model analysis shows that time delay plays a vital role in governing the dynamics of the system. It changes the stability behavior of the system into instability, even with the switching of stability. The direction and stability of Hopf-bifurcation are also studied by using normal form method and center manifold theorem. Finally, computer simulation and graphical illustrations have been carried out to support our theoretical investigations.

On the fuzzy difference equation xn = F(xn−1,xn−k)

In this paper, we study the global asymptotic behavior of the positive solutions of the following fuzzy difference equationxn=F(xn−1,xn−k),n∈{0,1,⋯}, under appropriate assumptions, where k∈{1,2,⋯} and the initial values x−k,x−k+1,⋯,x−1 are positive fuzzy numbers. We give sufficient conditions under which every positive solution of the above equation converges to a positive equilibrium.

Asymptotic Behavior of Discrete Time Fuzzy Single Species Model

This work is concerned with the qualitative behavior of discrete time single species model with fuzzy environment xn+1=xnexp⁡A-Bxn, n=0,1,2,…, where xn denotes the number of individuals of generation n, A is the intrinsic growth rate, and B is interpreted as the carrying capacity of the surrounding environment. xn is a sequence of positive fuzzy number. A,B and the initial value x0 are positive fuzzy numbers. Applying difference of Hukuhara (H-difference), the existence, uniqueness of the positive solution, and global asymptotic behavior of all positive solution with the model are obtained. Moreover a numerical example is presented to show the effectiveness of theoretic results obtained.

Asymptotic Expansion of the Solution of a Linear Parabolic Boundary-Value Problem in a Thin Starlike Joint

We consider a linear parabolic boundary-value problem in a thin 3D starlike joint that consists of a finite number of thin curvilinear cylinders connected through a domain (node) with diameter O(e). We develop a procedure for the construction of the complete asymptotic expansion of the solution as e → 0, i.e., in the case where the starlike joint is transformed into a graph. By using the method of matching of the asymptotic series, we deduce the limit problem (e = 0) on a graph with the corresponding Kirchhoff-type conjugation conditions at the vertex. We also prove asymptotic estimates, which enable us to trace the influence of the geometric shape of the node and the physical processes running in the node on the global asymptotic behavior of the solution.