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BIFURCATIONS IN A HUMAN MIGRATION MODEL OF SCHEURLE-SEYDEL TYPE-II: ROTATING WAVES
Kovacs, Sandor 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.1
This paper treats the conditions for the existence of rotating wave solutions of a system modelling the behavior of students in graduate programs at neighbouring universities near each other which is a modified form of the model proposed by Scheurle and Seydel. We assume that both types of individuals are continuously distributed throughout a bounded two-dimension spatial domain of two types (circle and annulus), across whose boundaries there is no migration, and which simultaneously undergo simple (Fickian) diffusion. We will show that at a critical value of a system-parameter bifurcation takes place: a rotating wave solution arises.
SPATIAL INHOMOGENITY DUE TO TURING BIFURCATION IN A SYSTEM OF GIERER-MEINHARDT TYPE
Sandor, Kovacs 한국전산응용수학회 2003 Journal of applied mathematics & informatics Vol.11 No.1
This paper treats the conditions for the existence and stability properties of stationary solutions of reaction-diffusion equations of Gierer-Meinhardt type, subject to Neumann boundary data. The domains in which diffusion takes place are of three types: a regular hexagon, a rectangle and an isosceles rectangular triangle. Considering one of the relevant features of the domains as a bifurcation parameter it will be shown that at a certain critical value a diffusion driven instability occurs and Turing bifurcation takes place: a pattern emerges.
Bifurcations in a human migration model of Scheurle-Seydel type--II: Rotating waves,
Sandor Kovacs 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.-
This paper treats the conditions for the existence of rotating wave solutions of a system modelling the behavior of students in graduate programs at neighbouring universities near each other which is a modified form of the model proposed by Scheurle and Seydel. We assume that both types of individuals are continuously distributed throughout a bounded two-dimension spatial domain of two types (circle and annulus), across whose boundaries there is no migration, and which simultaneously undergo simple (Fickian) diffusion. We will show that at a critical value of a systemparameter bifurcation takes place: a rotating wave solution arises.
ON AN ARITHMETIC INEQUALITY BY K. T. ATANASSOV
Jozsef Sandor,Lehel Kovacs 장전수학회 2010 Proceedings of the Jangjeon mathematical society Vol.13 No.3
Let d(n) denote the number of distinct divisors of n, and denote by Ψ(n) the Dedekind arithmetical function. We offer improvements and generalizations of Atanassov's inequality (see [1]) Ψ(n) ≥ d(n) ·√n