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Towards a Global Theory of Singularly Perturbed Dynamical Systems
Perturbed Dynamical System Theory
2015/8/25
Dynamical systems with multiple time scales arise naturally in many domains.
Models of neural systems provide the principal motivation for this
paper. Most of the previous mathematical analysis of q...
Uniform convergence analysis of an upwind finite difference approximations of an homogenous singularly perturbed boundary value problem using grid equidistribution
singular perturbation adaptive grid rate of convergence error estimate
2011/10/13
We derive varepsilon-uniform error estimates for two first-order upwind discretizations of a model inhomogeneous, second-order, singularly perturbed boundary value problem on a non-uniform grid. Here,...
Averaging approximation to singularly perturbed nonlinear stochastic wave equations
stochastic nonlinear wave equations averaging tightness martingale
2011/9/16
Abstract: An averaging method is applied to derive effective approximation to the following singularly perturbed nonlinear stochastic damped wave equation \nu u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on...
Positive solutions for singularly perturbed nonlinear elliptic problem on manifolds via Morse theory
singular perturbation nondegenerate critical points Morse theory
2011/2/28
Given (M, g0) we consider the problem −"2g0+hu + u = (u+)p−1 with (", h) ∈ (0, ¯") × B. Here B is a ball centered at 0 with radius in the Banach space of all Ck symmetric covaria...
Positive solutions of singularly perturbed nonlinear elliptic problem on Riemannian manifolds with boundary
Positive solutions of singularly perturbed nonlinear elliptic Riemannian manifolds boundary
2011/2/28
Let (M, g) be a smooth connected compact Riemannian manifold of finite dimension n ≥ 2 with a smooth boundary @M. We consider the problem −"2gu + u = |u|p−2u, u > 0 on M, @u @= 0 on @M w...
Asymptotic Limit of a Singularly Perturbed Stationary Diffusion Equation: The Case of a Limit Cycle
Diffusion Equation Limit Cycle
2010/11/23
A limit cycle for a nonlinear ordinary differential equation has a sustained, stationary oscillation in time; Any non-trivial stationary stochastic process also exhibits stationary oscillations in tim...
DISCRETE APPROXIMATIONS FOR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS WITH PARABOLIC LAYERS, II
2007/12/11
In his series of three papers we study
singularly perturbed (SP)
boundary value problems for equations of elliptic
and parabolic type.
For small values of the perturbation parameter
parabolic bou...
DISCRETE APPROXIMATIONS FOR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS WITH PARABOLIC LAYERS, III
2007/12/11
In this series of three papers we study
singularly perturbed (SP)
boundary value problems for equations of elliptic
and parabolic type.
For small values of the perturbation parameter
parabolic bo...
DISCRETE APPROXIMATIONS FOR SINGULARLY PERTURBED BOUNDARY VALUE PEOBLEMS WITH PARABOLIC LAYERS, I
2007/12/11
In this series of three papers we study
singularly perturbed (SP)
boundary value problems for equations of elliptic
and parabolic type.
For small values of the perturbation parameter
parabolic bo...
A Finite Element Method for Singularly Perturbed Reaction-diffusion Problems
finite element method singularly perturbed
2007/12/11
A finite element method is proposed for the singularly perturbed reaction-diffusion problem. An optimal error bound is derived, independent of the perturbation parameter.
Exponential Stability of Traveling Pulse Solutions of a Singularly Perturbed System ofIntegral Differential Equations Arising From Excitatory Neuronal Networks
Integral differential equations traveling pulse solutions exponential stability linear differential operators eigenvalue problems eigenvalue functions
2007/12/11
We establish the exponential stability of fast travelingpulse solutions to nonlinear singularly perturbed systems ofintegral differential equations arising from neuronal networks. Ithas been proved th...
Pseudo almost periodic solutions of a singularly perturbed differential equation with piecewise constant argument
Singular perturbation Pseudo-almost periodic solutions Pseudo-almost periodic sequences Piecewise constant argument
2007/12/11
Under suitable assumptions, the existence and the uniqueness of the pseudo-almost periodic solution for a singularly perturbed differential equation with piecewise constant argument are obtained. In a...
A CLASS OF NONLOCAL SINGULARLY PERTURBED PROBLEMS FOR NONLINEAR HYPERBOLIC DIFFERENTIAL EQUATION
Nonlocal problem nonlinear hy
2007/12/10
The nonlocal singularly perturbed problems for the hyperbolic differential equation are considered. Under suitable conditions, using the fixed point theorem, the asymptotic behavior of solution for th...
D-CONTROLLABILITY AND CONTROL OF MULTIPARAMETER AND MULTIPLE TIME-SCALE SINGULARLY PERTURBED SYSTEMS
Singularly perturbed systems multiparam
2007/12/10
摘要 Concepts of D-controllability and strong D-controllability are introduced, in terms of which the controllability of multiparameter and multiple timescale singularly perturbed systems is investigate...
A CLASS OF SINGULARLY PERTURBED REACTION DIFFUSION INTEGRAL DIFFERENTIAL SYSTEM
Reaction diffusion system sin
2007/12/10
In this paper a class of singularly perturbed initial boundary value problems for the reaction diffusion integral differential system are considered. Using the iteration method and the differential i...