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Title: | Fractal analysis of degenerate spiral trajectories of a class of ordinary differential equations | Authors: | HUZAK, Renato Vlah, Domagoj Zubrinic, Darko Zupanovic, Vesna |
Issue Date: | 2022 | Publisher: | ELSEVIER SCIENCE INC | Source: | APPLIED MATHEMATICS AND COMPUTATION, 438 (Art N° 127569) | Status: | Early view | Abstract: | In this paper we initiate the study of the Minkowski dimension, also called the box dimension, of degenerate spiral trajectories of a class of ordinary differential equations. A class of singularities of focus type with two zero eigenvalues (nilpotent or more degenerate) has been studied. We find the box dimension of a polynomial degenerate focus of type (n, n ) by exploiting the well-known fractal results for α-power spirals. In the general (m, n ) case, we formulate a conjecture about the box dimension of a degenerate focus using numerical experiments. Further, we reduce the fractal analysis of planar nilpotent contact points to the study of the box dimension of a slow-fast spiral generated by their “entry-exit” function. There exists a bijective correspondence between the box dimension of the slow-fast spirals and the codimension of contact points. We also construct a three-dimensional vector field that contains a degenerate spiral, called an elliptical power spiral, as a trajectory. | Keywords: | Box dimension (Minkowski dimension);Degenerate spiral trajectories;Geometric chirps;Turning points | Document URI: | http://hdl.handle.net/1942/38722 | ISSN: | 0096-3003 | e-ISSN: | 1873-5649 | DOI: | https://doi.org/10.1016/j.amc.2022.127569 | ISI #: | 000866507400001 | Datasets of the publication: | https://www.sciencedirect.com/science/article/pii/S0096300322006439?dgcid=coauthor | Rights: | 2022 Elsevier Inc. All rights reserved. | Category: | A1 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
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Fractal_analysis_of_degenerate_spiral_trajectories_of_a_class_of_ordinary_differential_equations.pdf | Non Peer-reviewed author version | 582.59 kB | Adobe PDF | View/Open |
Fractal_analysis_of_degenerate_spiral_trajectories_of_a_class_of_ordinary_differential_equations.pdf Restricted Access | Early view | 582.59 kB | Adobe PDF | View/Open Request a copy |
1-s2.0-S0096300322006439-main.pdf | 922.08 kB | Adobe PDF | View/Open |
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