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Description
The following dataset is connected with a map-based neuron model introduced by D. Chialvo (Chaos, Solitons & Fractals, 5 (3-4) 1995). The reduced version of this model is a one dimensional discrete system which describes the evolution of the membrane voltage when the value of the second variable, the recovery variable, is fixed. We have recently derived a theorem establishing a combinatorial condition for the orbit of the critical point of the reduced Chialvo map under which the model displays chaos (in the sense of Li-Yorke, Block-Coppel and Devaney). Further information can be found in the file Description_TopologicalChaosChialvo.pdf.
The dataset contains also the Matlab file (r_vs_k_up.m) which in a given discretized range of r and k values (where k is the input current) finds those (r,k) pairs for which the condition is satisfied and thus the model displays chaos. The program produces a figure with these values depicted and the Excel table where the first row has the values of r and the corresponding values of k, that satisfy the condition, are listed below in columns. Exemplary figure (Chaos_Parameters.png) and xlsx file (chaoticvalues.xlsx) are contained as well.
We remark that the program can be easily modified for any other unimodal interval map, for which our condition applies.
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 BYAttribution
Details
- Year of publication:
- 2021
- Verification date:
- 2021-11-03
- Dataset language:
- English
- Fields of science:
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- mathematics (Natural sciences)
- DOI:
- DOI ID 10.34808/by1g-e883 open in new tab
- Funding:
- Verified by:
- Gdańsk University of Technology
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