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Description
This dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "A database schema for the analysis of global dynamics of multiparameter systems" by Z. Arai, W. Kalies, H. Kokubu, K. Mischaikow, H. Oka, P. Pilarczyk, published in SIAM Journal on Applied Dynamical Systems (SIADS), Vol. 8, No. 3 (2009), pp. 757–789, doi: 10.1137/080734935.
The parameter space [8,37]✕[3,50]✕[0.5,0.9] was sampled at the resolution of 80✕80✕40. The phase space was sampled at the resolution of 2048✕2048. A collection of isolating neighborhoods that enclose Morse sets in a Morse decomposition was computed for each box of parameters, and a Conley-Morse graph was determined, with the Conley indices of the Morse sets computed where feasible. Clutching graphs between Morse decompositions found for adjacent boxes were also computed, and the parameter space was subdivided into classes of equivalent Morse decompositions, as described in the paper. The parallelization framework introduced in the paper "Parallelization method for a continuous property" by P. Pilarczyk was used in the computations, as published in Foundations of Computational Mathematics, Vol. 10, No. 1 (2010), 93–114, doi: 10.1007/s10208-009-9050-8.
The dataset contains the Morse decompositions found for all the parameter boxes. A collection of combinatorial Morse sets, that is, isolating neighborhoods of the actual Morse sets in each Morse decomposition, is encoded in terms of a PNG image. In this image, a single pixel corresponds to a square in the phase space. All the images are compressed together in the zipped archive file. The name of each file is in the format "pn_m_k.png", where n,m,k are the integer coordinates of the parameter box in the ranges: [0,79], [0,79], and [0,39], respectively. Each image is cropped in order to avoid the vast white area around the sets. Each combinatorial Morse set comprises of a collection of pixels drawn in a specific color. The colors used for the consecutive sets are listed at the bottom of the image as squares: black, blue, red, green, etc. The order is the same as in the corresponding Conley-Morse graphs available in a separate dataset. Note that the first set (black) is often a very small neighborhood of the origin that can be spotted as a single pixel at the bottom left corner of the image.
An interactive browser of all the Conley-Morse graphs and phase space portraits of the Morse decompositions provided in the current series of datasets is available at the address http://www.pawelpilarczyk.com/database/.
Dataset file
hexmd5(md5(part1)+md5(part2)+...)-{parts_count} where a single part of the file is 512 MB in size.Example script for calculation:
https://github.com/antespi/s3md5
File details
- License:
-
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CC BY-SAShare-alike
Details
- Year of publication:
- 2008
- Verification date:
- 2021-07-29
- Dataset language:
- English
- Fields of science:
-
- mathematics (Natural sciences)
- biological sciences (Natural sciences)
- DOI:
- DOI ID 10.34808/8xba-v953 open in new tab
- Series:
- Verified by:
- Gdańsk University of Technology
Keywords
- Dynamical Systems
- Rigorous Numerical Methods
- Conley Index
- Morse Decomposition
- Population Models
- Population Dynamics
- Scientific Computation
References
- publication A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems
- publication Parallelization Method for a Continuous Property
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