On a singular perturbed differential delay equation
On Chaotic Subthreshold Oscillations in a Simple Neuronal Model
In a simple FitzHugh-Nagumo neuronal model with one fast and two slow variables, a sequence of period-doubling bifurcations for small-scale oscillations precedes the transition into the spiking regime. For a wide range of values of the timescale separation parameter, this scenario is recovered numerically. Its relation to the singularly perturbed integrable system is discussed.
On Newton's polygons, Gröbner bases and series expansions of perturbed polynomial programs
In this note we consider a perturbed mathematical programming problem where both the objective and the constraint functions are polynomial in all underlying decision variables and in the perturbation parameter ε. Recently, the theory of Gröbner bases was used to show that solutions of the system of first order optimality conditions can be represented as Puiseux series in ε in a neighbourhood of ε = 0. In this paper we show that the determination of the branching order and the order of the pole (if...
On perturbation of continuous maps
In [1], the concept of singular isolating neighborhoods for a continuous family of continuous maps was presented. The work was based on Conley's result for a continuous family of continuous flows (cf. [2]). In this note, we study a particular family of continuous maps to illustrate the results in [1].
On Pontryagin-Rodygin's theorem for convergence of solutions of slow and fast systems.
On singularly perturbed ordinary differential equations with measure-valued limits
On the singular limit in a phase field model of phase transitions
On Tykhonov's theorem for convergence of solutions of slow and fast systems.