On invariant manifolds of saddle points for 3D multistable models

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In dynamical systems a particular solution is completely determined by the parameters considered and the initial conditions. Indeed, when the model shows a multistability, starting from different initial state, the trajectories can evolve towards different attractors. The invariant manifolds of the saddle points separate the vector field into the basins of attraction of different stable equilibria. The aim of this work is the reconstruction of these separation surfaces in order to know in advance the geometry of the basins. In this paper three-dimensional models with three or more stable fixed points is investigated. To this purpose a procedure for the detection of the scattered data lying on the manifolds is proposed. Then a Moving Least Squares meshfree method is involved to approximate the surfaces. Numerical results are presented in order to assess the method.
Original languageEnglish
Title of host publicationComputational and Mathematical Methods in Science and Engineering
Pages874-880
Number of pages7
Volume2
Publication statusPublished - 2017

Fingerprint

Invariant Manifolds
Saddlepoint
3D Model
Multistability
Moving Least Squares
Scattered Data
Meshfree Method
Basin of Attraction
Particular Solution
Least Square Method
Attractor
Vector Field
Initial conditions
Dynamical system
Fixed point
Trajectory
Numerical Results
Three-dimensional
Model

Cite this

Francomano, E., & Paliaga, M. (2017). On invariant manifolds of saddle points for 3D multistable models. In Computational and Mathematical Methods in Science and Engineering (Vol. 2, pp. 874-880)

On invariant manifolds of saddle points for 3D multistable models. / Francomano, Elisa; Paliaga, Marta.

Computational and Mathematical Methods in Science and Engineering. Vol. 2 2017. p. 874-880.

Research output: Chapter in Book/Report/Conference proceedingChapter

Francomano, E & Paliaga, M 2017, On invariant manifolds of saddle points for 3D multistable models. in Computational and Mathematical Methods in Science and Engineering. vol. 2, pp. 874-880.
Francomano E, Paliaga M. On invariant manifolds of saddle points for 3D multistable models. In Computational and Mathematical Methods in Science and Engineering. Vol. 2. 2017. p. 874-880
Francomano, Elisa ; Paliaga, Marta. / On invariant manifolds of saddle points for 3D multistable models. Computational and Mathematical Methods in Science and Engineering. Vol. 2 2017. pp. 874-880
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