Recurrence times in the Morse sets for a two-dimensional discrete neuron model (low resolution)

This dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper “Topological-numerical analysis of a two-dimensional discrete neuron model” by Paweł Pilarczyk, Justyna Signerska-Rynkowska and Grzegorz Graff. A preprint of this paper is available at https://doi.org/10.48550/arXiv.2209.03443.
The parameter space a=0.89, b∊[0,0.5], c=0.28, k∊[0.017,0.027] was sampled at the resolution of 200×50. The phase space [−0.1,7.5] × [−1.3,2.7] was sampled at the resolution of 256×256. 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 dataset contains the integer coordinates of all the elements (boxes) of the Morse decompositions found for all the parameter boxes, together with recurrence times computed for each element. The order of the sets in each Morse decomposition is the same as in the corresponding Conley-Morse graphs available in a separate dataset. The data format is very intuitive: the integer coordinates of each box are enclosed in parentheses and separated with a comma. The computed recurrence time follows the closing parenthesis after the space. For example, the line “(3,151) 12“ indicates the box (3,151) with recurrence time 12.
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 https://www.pawelpilarczyk.com/neuron/.