A class of singularly perturbed evolution systems.
A singular perturbation method for saddle connections and subharmonics of certain nonlinear differential equations with fixed saddle points.
Saddle connections and subharmonics are investigated for a class of forced second order differential equations which have a fixed saddle point. In these equations, which have linear damping and a nonlinear restoring term, the amplitude of the forcing term depends on displacement in the system. Saddle connections are significant in nonlinear systems since their appearance signals a homoclinic bifurcation. The approach uses a singular perturbation method which has a fairly broad application to saddle...
A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces
We consider a class of singularly perturbed systems of semilinear parabolic differential inclusions in infinite dimensional spaces. For such a class we prove a Tikhonov-type theorem for a suitably defined subset of the set of all solutions for ε ≥ 0, where ε is the perturbation parameter. Specifically, assuming the existence of a Lipschitz selector of the involved multivalued maps we can define a nonempty subset of the solution set of the singularly perturbed system. This subset is the set of...
Constructive method for solving a nonlinear singularly perturbed system of differential equations in critical case.
Continuum limits of particles interacting via diffusion.
Entrée-sortie dans un tourbillon
On étudie un champ de vecteurs lent-rapide de nommé tourbillon pour lequel on démontre l’existence d’une fonction entrée-sortie.
Estimates of the lower exponent of a two-dimensional linear system under Perron perturbations.
Everted equilibria of a spherical cap : a singular perturbation method
Exponential stability for a class of singularly perturbed Itô differential equations.
Exponential stability for singularly perturbed systems with state delays.
Higher Order Methods for a Singularly Perturbed Problem.
Integral Manifolds and Bounded Solutions of Singularly Perturbed Systems of Impulsive Differential Equations
Sufficient conditions for the existence of bounded solutions of singularly perturbed impulsive differential equations are obtained. For this purpose integral manifolds are used.
Nonlinear singularly perturbed systems of differential equations: A survey.
Novel method for generalized stability analysis of nonlinear impulsive evolution equations
In this paper, we discuss some generalized stability of solutions to a class of nonlinear impulsive evolution equations in the certain piecewise essentially bounded functions space. Firstly, stabilization of solutions to nonlinear impulsive evolution equations are studied by means of fixed point methods at an appropriate decay rate. Secondly, stable manifolds for the associated singular perturbation problems with impulses are compared with each other. Finally, an example on initial boundary value...
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