scholarly journals Existence and asymptotic stability of periodic solution for evolution equations with delays

2011 ◽  
Vol 261 (5) ◽  
pp. 1309-1324 ◽  
Author(s):  
Yongxiang Li
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Evolution Equations

Asymptotic stability for nonlinear PDEs with hysteresis

1994 ◽  
Vol 5 (1) ◽  
pp. 39-56 ◽  
Author(s):  
Nobuyuki Kenmochi ◽  
Augusto Visintin
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Evolution Equations ◽  
Stable Equilibrium ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Nonlinear Pdes ◽  
Independent Function ◽  
Forcing Term ◽  
Stability Of The Solution

Nonlinear evolution equations including hysteresis functionals are studied. It is the purpose of this paper to investigate the asymptotic stability of the solution as time t → + ∞. In the case when the forcing term of the equation tends to a time-independent function as t → + ∞, we shall show that the solution stabilizes at + ∞ and the system is asymptotically stable (equilibrium stability). In the case when the forcing term is periodic in time, we shall show that there is at least one periodic solution and that in some restricted cases the periodic solution is unique.

scholarly journals Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Giovanni Colombo ◽  
Paolo Gidoni ◽  
Emilio Vilches
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Periodic Solutions ◽  
Finite Time ◽  
Dry Friction ◽  
Average Velocity ◽  
Well Posedness ◽  
Asymptotic Velocity ◽  
Sweeping Processes

<p style='text-indent:20px;'>We study the asymptotic stability of periodic solutions for sweeping processes defined by a polyhedron with translationally moving faces. Previous results are improved by obtaining a stronger <inline-formula><tex-math id="M1">\begin{document}$ W^{1,2} $\end{document}</tex-math></inline-formula> convergence. Then we present an application to a model of crawling locomotion. Our stronger convergence allows us to prove the stabilization of the system to a running-periodic (or derivo-periodic, or relative-periodic) solution and the well-posedness of an average asymptotic velocity depending only on the gait adopted by the crawler. Finally, we discuss some examples of finite-time versus asymptotic-only convergence.</p>

PERMANENCE AND THE EXISTENCE OF THE PERIODIC SOLUTION OF THE NON-AUTONOMOUS TWO-SPECIES COMPETITIVE MODEL WITH STAGE STRUCTURE

2004 ◽  
Vol 07 (03n04) ◽  
pp. 385-393 ◽  
Author(s):  
GUANGZHAO ZENG ◽  
LANSUN CHEN ◽  
LIHUA SUN ◽  
YING LIU
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Periodic System ◽  
Stage Structure ◽  
Competitive Model

This paper considers a non-autonomous competitive two-species model with stage structure in one species. The conditions of permanence obtained. Furthermore, the existence and asymptotic stability of the periodic solution are proved under some assumptions if this model turns out to be a periodic system.

Dynamical Behaviors for a Predator-Prey System with State-Dependent Impulsive Effects

2011 ◽  
Vol 130-134 ◽  
pp. 385-390
Author(s):  
Ling Zhen Dong ◽  
Lan Sun Chen
Keyword(s):  
Dynamical System ◽  
Periodic Solution ◽  
Asymptotic Stability ◽  
Impulsive System ◽  
Impulsive Effects ◽  
Predator Prey ◽  
Dynamical Behaviors ◽  
Prey System ◽  
State Dependent ◽  
Impulsive Model

With some theory about continuous and impulsive dynamical system, an impulsive model based on a special predator-prey system is considered. We assume that the impulsive effects occur when the density of the prey reaches a given value. For such a state-dependent impulsive system, the existence, uniqueness and orbital asymptotic stability of an order-1 periodic solution are discussed. Further, the existence of an order-2 periodic solution is also obtained, and persistence of the system is investigated.

scholarly journals An application of topological degree to the periodic competing species problem

1986 ◽  
Vol 28 (2) ◽  
pp. 202-219 ◽  
Author(s):  
Carlos Alvarez ◽  
Alan C. Lazer
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Lower Bounds ◽  
Topological Degree ◽  
Upper And Lower Bounds ◽  
Species Problem ◽  
Competing Species ◽  
Right Hand ◽  
The Right ◽  
Stability Of The Solution

AbstractWe consider the Volterra-Lotka equations for two competing species in which the right-hand sides are periodic in time. Using topological degree, we show that conditions recently given by K. Gopalsamy, which imply the existence of a periodic solution with positive components, also imply the uniqueness and asymptotic stability of the solution. We also give optimal upper and lower bounds for the components of the solution.

scholarly journals Global asymptotic stability in a periodic Lotka-Volterra system

1985 ◽  
Vol 27 (1) ◽  
pp. 66-72 ◽  
Author(s):  
K. Gopalsamy
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Stable Periodic Solution ◽  
Volterra System ◽  
Periodic Coefficients ◽  
Globally Asymptotically Stable ◽  
Stable Periodic

AbstractA set of easily verifiable sufficient conditions are obtained for the existence of a globally asymptotically stable periodic solution in a Lotka-Volterra system with periodic coefficients.

Dynamics of a non-autonomous ratio-dependent predator—prey system

2003 ◽  
Vol 133 (1) ◽  
pp. 97-118 ◽  
Author(s):  
Meng Fan ◽  
Qian Wang ◽  
Xingfu Zou
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Positive Periodic Solution ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Predator Prey ◽  
Prey System ◽  
Autonomous Case ◽  
Positive Almost Periodic Solution ◽  
Ratio Dependent

We investigate a non-autonomous ratio-dependent predator–prey system, whose autonomous versions have been analysed by several authors. For the general non-autonomous case, we address such properties as positive invariance, permanence, non-persistence and the globally asymptotic stability for the system. For the periodic and almost-periodic cases, we obtain conditions for existence, uniqueness and stability of a positive periodic solution, and a positive almost-periodic solution, respectively.

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