Asymptotic and chaotic solutions of a singularly perturbed Nagumo-type equation

Periodic solutions of a singularly perturbed delay differential equation

A singularly perturbed differential delay equation of the form ẋ(t) = −x(t)+ f (x(t − 1), λ) (1) exhibits slowly oscillating periodic solutions (SOPS) near the first period-doubling bifurcation point of the underlying map (obtained by setting = 0). For extremely small values of , these periodic solutions resemble square waves, which consist of sharp, O( ) transition layers connecting intervals ...

EXISTENCE AND ASYMPTOTIC ANALYSIS OF SOLUTIONS OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS by

the investigation of the relationship between type a and type b personalities and quality of translation

چکیده ندارد.

Weakly Non-local Solitary Wave Solutions of a Singularly Perturbed Boussinesq Equation

We study the singularly perturbed (sixth-order) Boussinesq equation recently introduced by Daripa and Hua [Appl. Math. Comput. 101 (1999), 159-207]. This equation describes the bi-directional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for Bond number less than but very close to 1/3. On the basis of far-field analyses and heuristic arguments, ...

Existence of Chaos for a Singularly Perturbed NLS Equation

The work [1] is generalized to the singularly perturbed nonlinear Schrödinger (NLS) equation of which the regularly perturbed NLS studied in [1] is a mollification. Specifically, the existence of Smale horseshoes and Bernoulli shift dynamics is established in a neighborhood of a symmetric pair of Silnikov homoclinic orbits under certain generic conditions, and the existence of the symmetric pai...