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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] was sampled at the resolution of 50✕50. 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 computed classes of parameters that yield equivalent Morse decompositions, also named "continuation classes" in the paper. Only classes of cardinality at least 2 are provided. Each of the continuation classes is defined in a text file "cont*.cub" with the "*" sign replaced by the consecutive number of each class, in the descending order by class cardinality. Each file contains a list of parameter boxes contained in the class. Each box is defined as a comma-separated list of coordinates, with the list enclosed in parentheses. Each box in the file is listed in a separate line. The integer coordinates are both in the range [0,49]. Note that classes of cardinality 1 are not included, as they can be easily determined by verifying which boxes from {0,…,49}✕{0,…,49} are absent in the union of the classes included in the collection.
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:
- 2021
- Verification date:
- 2021-07-29
- Dataset language:
- English
- Fields of science:
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- mathematics (Natural sciences)
- biological sciences (Natural sciences)
- DOI:
- DOI ID 10.34808/9zhd-4f14 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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