We consider a complex autonomously driven single limit cycle oscillator with delayed feedback.The original model is translated to a two-dimensional system.Through a nonstandard finite-difference (NSFD) schemewe study the dynamics of this resulting system. The stability of the equilibriumof themodel is investigated by analyzing the characteristic equation. In the two-dimensional discrete model, ...

This paper provides a new proof of the consistency of a formal system similar to the one presented by Chuaqui and Suppes in 2, 9]. First, a simpler, yet in some respects stronger, system, called Elementary Re-cursive Nonstandard Analysis (ERNA) will be provided. Indeed, it will be shown that ERNA proves the main axioms of the Chuaqui and Sup-pes system. Then a nitary consistency proof of ERNA w...

This paper provides a new proof of the consistency of the formal system presented by Chuaqui and Suppes in [2, 9). First, a simpler, yet stronger, system, called Elementary Recursive Nonstandard Analysis, ERNA, will be provided. Indeed, it will be shown that ERNA proves all of the theorems of the Chuaqui and Suppes system. Then a finitary consistency proof of ERNA dl be given; in particular, we...

This paper presents analysis of data aggregated from three experiments, investigating whether there are social differences in the processing of sociolinguistic variation. Three self-paced reading experiments tested the processing of variable subject-verb agreement in English. Sentences appeared in one of three agreement conditions: standard [singular+doesn’t] or [plural+don’t], nonstandard [sin...

Let q = pr be a prime power, and let f(x) = xm − σm−1x m−1 − · · · − σ1x− σ0 be an irreducible polynomial over the finite field GF(q) of size q. A zero ξ of f is called nonstandard (of degree m) over GF(q) if the recurrence relation um = σm−1um−1 + · · · + σ1u1 + σ0u0 with characteristic polynomial f can generate the powers of ξ in a nontrivial way, that is, with u0 = 1 and f(u1) 6= 0. In 2003,...

A numerical scheme for a SIS epidemic model with a delay is constructed by applying a nonstandard finite difference (NSFD) method. The dynamics of the obtained discrete system is investigated. First we show that the discrete system has equilibria which are exactly the same as those of continuous model. By studying the distribution of the roots of the characteristics equations related to the lin...

This paper concerns with the modeling and construction of a fifth order method for two dimensional acoustic wave equation in heterogenous media. The method is based on a standard discretization of the problem on smooth regions and a nonstandard method for nonsmooth regions. The construction of the nonstandard method is based on the special treatment of the interface using suitable jump conditio...

It is shown that the nonstandard representatives of Schwartz-distributions, as introduced by K. D. Stroyan and W. A. J. Luxemburg in their book Introduction to the theory of infinitesimals [5], are locally equal to a finite-order derivative of a finite-valued and S-continuous function. By ‘equality’, we mean a pointwise equality, not an equality in a distributional sense. This proves a conjectu...