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Approximation of limit cycle of differential systems with variable coefficients

Masakazu Onitsuka (2023)

Archivum Mathematicum

The behavior of the approximate solutions of two-dimensional nonlinear differential systems with variable coefficients is considered. Using a property of the approximate solution, so called conditional Ulam stability of a generalized logistic equation, the behavior of the approximate solution of the system is investigated. The obtained result explicitly presents the error between the limit cycle and its approximation. Some examples are presented with numerical simulations.

Approximation of mixed type functional equations in $p$ -Banach spaces.

Zolfaghari, S. (2010)

The Journal of Nonlinear Sciences and its Applications

AQCQ-functional equation in non-Archimedean normed spaces.

Gordji, M.Eshaghi, Khodabakhsh, R., Jung, S.-M., Khodaei, H. (2010)

Abstract and Applied Analysis

Arithmetic based fractals associated with Pascal's triangle.

T.W. Gamelin, Mamiron A. Mnatsakanian (2005)

Publicacions Matemàtiques

Our goal is to study Pascal-Sierpinski gaskets, which are certain fractal sets defined in terms of divisibility of entries in Pascal's triangle. The principal tool is a carry rule for the addition of the base-q representation of coordinates of points in the unit square. In the case that q = p is prime, we connect the carry rule to the power of p appearing in the prime factorization of binomial coefficients. We use the carry rule to define a family of fractal subsets Bqr of the unit square, and we...

Arithmetic properties of the solutions of a class of functional equations.

J.H. Loxton, A.J. van der Poorten (1982)

Journal für die reine und angewandte Mathematik

Arithmetical aspects of certain functional equations

Lutz G. Lucht (1997)

Acta Arithmetica

The classical system of functional equations $1 / n \sum_{ν = 0}^{n - 1} F ((x + ν) / n) = n^{- s} F (x)$ (n ∈ ℕ) with s ∈ ℂ, investigated for instance by Artin (1931), Yoder (1975), Kubert (1979), and Milnor (1983), is extended to $1 / n \sum_{ν = 0}^{n - 1} F ((x + ν) / n) = \sum_{d = 1}^{\infty} λ_{n} (d) F (d x)$ (n ∈ ℕ) with complex valued sequences $λ_{n}$ . This leads to new results on the periodic integrable and the aperiodic continuous solutions F:ℝ₊ → ℂ interrelating the theory of functional equations and the theory of arithmetic functions.

Arithmetical sequences and systems of functional equations.

Lutz G. Lucht (1997)

Aequationes mathematicae

Associativity in a Class of Operations on Spaces of Distribution Functions.

M.J. Frank (1975)

Aequationes mathematicae

Asymptotic analysis of a class of functional equations and applications

P. J. Grabner, H. Prodinger, R. F. Tichy (1993)

Journal de théorie des nombres de Bordeaux

Flajolet and Richmond have invented a method to solve a large class of divide-and-conquer recursions. The essential part of it is the asymptotic analysis of a certain generating function for $z \to \infty$ by means of the Mellin transform. In this paper this type of analysis is performed for a reasonably large class of generating functions fulfilling a functional equation with polynomial coefficients. As an application, the average life time of a party of $N$ people is computed, where each person advances one...