Approximating basins of attraction for dynamical systems via stable radial bases

Journal Article · Wed Jun 08 00:00:00 EDT 2016 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.4952177· OSTI ID:22608994

Cavoretto, R.; De Rossi, A.; Perracchione, E. ^[1]; De Marchi, S.; Santin, G. ^[2]

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1. Department of Mathematics “Giuseppe Peano”, University of Torino, via Carlo Alberto 10, 10123 Torino (Italy)
2. Department of Mathematics, University of Padova, via Trieste 63, 35121 Padova (Italy)

In applied sciences it is often required to model and supervise temporal evolution of populations via dynamical systems. In this paper, we focus on the problem of approximating the basins of attraction of such models for each stable equilibrium point. We propose to reconstruct the basins via an implicit interpolant using stable radial bases, obtaining the surfaces by partitioning the phase space into disjoint regions. An application to a competition model presenting jointly three stable equilibria is considered.

• OSTI ID: 22608994
• Journal Information: AIP Conference Proceedings, Vol. 1738, Issue 1; Conference: ICNAAM 2015: International conference of numerical analysis and applied mathematics 2015, Rhodes (Greece), 22-28 Sep 2015; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
EQUILIBRIUM
EVOLUTION
FORECASTING
PARTITION
PHASE SPACE
POPULATIONS
SURFACES