The reduced 1D Poisson-Nernst-Planck (PNP) model of artificial nanopores in the presence of a permanent charge on the channel wall is studied. More specifically, we consider the limit where the channel length exceed much the Debye screening length and channel’s charge is sufficiently small. Ion transport is described by the nonequillibrium steady-state solution of the PNP system within a singul...

We consider the approximation of systems of singularly perturbed reaction-diffusion equations, with the finite element method. The solution to such problems contains, in general, boundary layers which overlap and interact, and the numerical approximation must take this into account in order for the resulting scheme to converge uniformly with respect to the singular perturbation parameters. In t...

This paper presents the design of an additive fault tolerant control for nonlinear time-invariant singularly perturbed systems against actuator faults based on Lyapunov redesign principle. The overall system is reduced into subsystems with fast and slow dynamic behavior using singular perturbation method. The time scale reduction is carried out when the singular perturbation parameter is set to...

For a wide range of parameters, we study travelling waves in a diffusive version of the Holling-Tanner predator-prey model from population dynamics. Fronts are constructed using geometric singular perturbation theory and the theory of rotated vector fields. We focus on the appearance of the fronts in various singular limits. In addition, periodic travelling waves of relaxation oscillation type ...

We show the existence of positive solutions for a class of singular elliptic systems with convection term. The approach combines sub and supersolution method with the pseudomonotone operator theory and perturbation arguments involving singular terms. 2000 Mathematics Subject Classi…cation: 35J50, 35J60, 35J75

We investigate the singular Weyl–Titchmarsh m-function of perturbed spherical Schrödinger operators (also known as Bessel operators) under the assumption that the perturbation q(x) satisfies xq(x) ∈ L(0, 1). We show existence plus detailed properties of a fundamental system of solutions which are entire with respect to the energy parameter. Based on this we show that the singular m-function bel...

In this work, we extended the application of “the modified reductive perturbation method” to long water waves and obtained the governing equations of Korteweg – de Vries (KdV) hierarchy. Seeking localized travelling wave solutions to these evolution equations we have determined the scale parameter g1 so as to remove the possible secularities that might occur. To indicate the effectiveness and t...

In this paper we use perturbation theory approach to analyze using truncated balanced realization (TBR) linear reduction in a Trajectory-Piecewise linear (TPWL) nonlinear model reduction method. We show that the most important factor affecting perturbation properties of the reduction basis of TBR is a spacing of Hankel singular values. The result is applied to choosing an order of reduction basis.

We construct unbounded strange attractors for vector fields in R that are robust transitive under uniformly small perturbations. Their geometry is reminiscent of geometric Lorenz and other singular hyperbolic attractors, but they contain no equilibria.

Consider the singular perturbation problem for εu(t; ε) + u(t; ε) = Au(t; ε) + ∫ t 0 K(t− s)Au(s; ε) ds+ f(t; ε) , where t ≥ 0, u(0; ε) = u0(ε), u (0; ε) = u1(ε), and w(t) = Aw(t) + ∫ t 0 K(t− s)Aw(s)ds+ f(t) , t ≥ 0 , w(0) = w0 , in a Banach space X when ε → 0. Here A is the generator of a strongly continuous cosine family and a strongly continuous semigroup, and K(t) is a bounded linear opera...