Morse decompositions for a two-dimensional discrete neuron model (full range)

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∊[0,1], c=0.28, k∊[0.0,0.2] was sampled at the resolution of 100×100. The phase space [−0.1,9] × [−5,3] was sampled at the resolution of 1024×1024. 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 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.png", where n,m are the integer coordinates of the parameter box, both starting with 0. 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.
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/.