6533b7dbfe1ef96bd1270192
RESEARCH PRODUCT
Detecting tri‐stability of 3D models with complex attractors via meshfree reconstruction of invariant manifolds of saddle points
Marta PaliagaElisa Francomanosubject
Dynamical systems Invariant manifolds Separatrix Meshfree method Moving Least Squares.Dynamical systems theorySeparatrixGeneral MathematicsMathematical analysisGeneral Engineering3d model010103 numerical & computational mathematics01 natural sciences010101 applied mathematicsSettore MAT/08 - Analisi NumericaSaddle pointAttractor0101 mathematicsMoving least squaresInvariant (mathematics)Mathematicsdescription
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 multi-stable the trajectories approach different stable states, depending on the initialmconditions. The aim of this work is the detection of the invariant manifolds of thesaddle 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-04-27 | Mathematical Methods in the Applied Sciences |