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Your search keyword '"Panchuk, Anastasiia"' showing total 2 results
Start Over Author "Panchuk, Anastasiia" Topic attractors (mathematics)
2 results on '"Panchuk, Anastasiia"'

1. A financial market model with two discontinuities: Bifurcation structures in the chaotic domain.

Author

Panchuk, Anastasiia, Sushko, Iryna, and Westerhoff, Frank

Subjects
*FINANCIAL markets, *PIECEWISE linear approximation, *CHAOS theory, *BIFURCATION theory, *ATTRACTORS (Mathematics)
Abstract

We continue the investigation of a one-dimensional piecewise linear map with two discontinuity points. Such a map may arise from a simple asset-pricing model with heterogeneous speculators, which can help us to explain the intricate bull and bear behavior of financial markets. Our focus is on bifurcation structures observed in the chaotic domain of the map's parameter space, which is associated with robust multiband chaotic attractors. Such structures, related to the map with two discontinuities, have been not studied before. We show that besides the standard bandcount adding and bandcount incrementing bifurcation structures, associated with two partitions, there exist peculiar bandcount adding and bandcount incrementing structures involving all three partitions. Moreover, the map's three partitions may generate intriguing bistability phenomena. [ABSTRACT FROM AUTHOR]

Published
2018
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2. Modeling learning and teaching interaction by a map with vanishing denominators: Fixed points stability and bifurcations.

Author

Merlone, Ugo, Panchuk, Anastasiia, and van Geert, Paul

Subjects
*TEACHING models, *ATTRACTORS (Mathematics), *POINT set theory
Abstract

Among the different dynamical systems which have been considered in psychology, those modeling the dynamics of learning and teaching interaction are particularly important. In this paper we consider a well known model of proximal development and analyze some of its mathematical properties. The dynamical system we study belongs to a class of 2D noninvertible piecewise smooth maps characterized by vanishing denominators in both components. We determine focal points, among which the origin is particular since its prefocal set contains this point itself. We also find fixed points of the map and investigate their stability properties. Finally, we consider map dynamics for two sample parameter sets, providing plots of basins of attraction for coexisting attractors in the phase plane. We emphasize that in the first example there exists a set of initial conditions of non-zero measure, whose orbits asymptotically approach the focal point at the origin. [ABSTRACT FROM AUTHOR]

Published
2019
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