2018
DOI: 10.1002/mma.4889
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Detecting tri‐stability of 3D models with complex attractors via meshfree reconstruction of invariant manifolds of saddle points

Abstract: 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 met… Show more

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Cited by 4 publications
(3 citation statements)
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“…By adopting the smooth and infinitely di↵erentiable Gaussian as kernel function we make use of the improved fast Gauss transform (IFGT) [17,18] for all the summations in (7) and (8). In this way the original fast Gauss transform by Greengard and Strain [9] is considerably improved both in term of computational cost and in accuracy.…”
Section: Fundamental Of the Fast Summationmentioning
confidence: 99%
See 1 more Smart Citation
“…By adopting the smooth and infinitely di↵erentiable Gaussian as kernel function we make use of the improved fast Gauss transform (IFGT) [17,18] for all the summations in (7) and (8). In this way the original fast Gauss transform by Greengard and Strain [9] is considerably improved both in term of computational cost and in accuracy.…”
Section: Fundamental Of the Fast Summationmentioning
confidence: 99%
“…Despite the success of the mesh based methods in the analysis of widely areas of the engineering and physical science a number of faults in handling physical problems occurs involving large deformations, high gradients or moving discontinuities. Recently, the new generation of so-called meshfree methods has emerged and is profoundly influencing many branches of applied science [4,6,7,12]. One of the most distinguished feature about these methods is that no explicit mesh is needed in the formulation.…”
Section: Introductionmentioning
confidence: 99%
“…In recent years these methods have received a strong interest emerging as valid computational alternatives in numerous problems, from different areas of science and engineering, that require the numerical solution of integral equations or PDEs with different boundary conditions [3,4,5,6,7]. Applications can be found in geodesy and mapping [8], geoscience [9], metereology [10], computer graphics [11], signal and image processing [12], computational finance [13,14], learning theory [15,16,17], biomathematics [18,19,20]. Many of these applications involve function approximation or need derivative estimation at any data location with any known data distribution in the problem domain.…”
Section: Introductionmentioning
confidence: 99%