Detecting tri‐stability of 3D models with complex attractors via meshfree reconstruction of invariant manifolds of saddle points

In mathematical modeling, it is often required the analysis of the vector field topology in order to predict the evolution of the variables involved. When a dynamical system is multistable, the trajectories approach different stable states, depending on the initial conditions. The aim of this work i...

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Published inMathematical methods in the applied sciences Vol. 41; no. 17; pp. 7450 - 7458
Main Authors Francomano, Elisa, Paliaga, Marta
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 30.11.2018
Subjects
Attractors (mathematics)
dynamical systems
Economic models
Fields (mathematics)
Initial conditions
invariant manifolds
Invariants
Manifolds (mathematics)
Mathematical models
meshfree method
Meshless methods
moving least squares
Saddle points
separatrix
Three dimensional models
Toruses
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Summary:In mathematical modeling, it is often required the analysis of the vector field topology in order to predict the evolution of the variables involved. When a dynamical system is multistable, the trajectories approach different stable states, depending on the initial conditions. The aim of this work is the detection of the invariant manifolds of the saddle points to analyze the boundaries of the basins of attraction. Once that a sufficient number of separatrix points is found, a moving least squares meshfree method is involved to reconstruct the separatrix manifolds. Numerical results are presented to assess the method referring to tri‐stable models with complex attractors such as limit cycles or limit tori.
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content type line 14
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.4889