Search results for " Invariant manifolds"
showing 3 items of 3 documents
On invariant manifolds of saddle points for 3D multistable models
2017
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 …
Detecting tri‐stability of 3D models with complex attractors via meshfree reconstruction of invariant manifolds of saddle points
2018
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 o…
Broglie and Young, visionaries who shed light in the polar topology that grounds our reality: a hypothesis
2020
Una observación matemática que relaciona los patrones fractales y la operación de convolución en el contexto del procesamiento de imágenes digitales interrumpió una investigación que nos lleva a plantear la hipótesis de que el concepto de onda de materia (o dualidad onda-partícula) se encuentra en la dicotomía entre el par débil y un topología fuerte en el ámbito del marco de atractores singulares continuos en ninguna parte diferenciables y el concepto de fotón-solitón de Vigier. Tal inferencia parece ser más evidente en la interpretación de Broglie-Bohm de la mecánica cuántica en el cruce de características locales x globales. De esto se deduce también que la relación de los fenómenos natu…