Singularly perturbed systems of ordinary differential equations arise in many biological, physical and chemical systems. We present an example of a singularly perturbed system of ordinary differential equations that arises as a model of the electrical potential across the cell membrane of a neuron. We describe two periodic solutions of this example that were numerically computed using continuat...

1285 small parameter " > 0, has been established. This proposition is based on the assumption of the stabilizability of the boundary-layer system. It was also shown that this connection is only one-direction valid, i.e., the controllability of the reduced-order and boundary-layer systems always yields the controllability of the original system, but not vice versa. The criterion of the impulse-f...

Novel rational spectral collocation is presented in combination with singularity separation method for the second-order singularly perturbed boundary-value problems. The solution form u = w + υ; where of corresponding third problem and υ a singular function explicit expression. auxiliary solved by combined asymptotic theory (RSCAT). According to analysis, parameters sinh-transformation can be d...

One of directions in the development Lomov’s regularization method is approach related to holomorphic singularly perturbed problems, which allows one construct solutions such problems form series powers a small parameter that converge usual sense. For boundary-value problem pseudo-holomorphic continuation very urgent. In this paper, we examine for Tikhonov system and give conditions existence i...