DOI: 10.34808/n997-gy19
title: Continuation classes for a population model with harvesting. Case He-Se: Equal harvesting and equal survival rates of juveniles and adults

description: This dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
The purpose of the research was to analyze the effect of constant effort harvesting upon global dynamics of the discrete-time population model with juvenile and adult stages described in the paper, with a Ricker-type nonlinearity. The following parameters of the dynamical system were considered:
ha, hj – harvesting rates for adults and juveniles, respectivelysa, sj – survival rates of adults and juveniles, respectively
A few different scenarios were considered, each called a specific case. The current dataset contains data for Case He-Se: Equal harvesting and equal survival rates of juveniles and adults, that is:
hj = hasj = sa(ha,sa) ∈ [0,1]✕[0,1]
The computations followed the general scheme explained 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, and P. Pilarczyk, published in SIAM J. Appl. Dyn. Syst., Vol. 8, No. 3 (2009), 757–789, doi: 10.1137/080734935.
The parameter space [0,1]✕[0,1] was sampled at the resolution of 500✕500. The phase space [0,1.35]✕[0,1.35] 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. The complete computation on a Quad-Core AMD Opteron™ Processor 2376 2.3 GHz with Debian GNU/Linux took 1,169 hours of CPU time, and the memory usage was up to 405 MB. The parallelization framework introduced in the paper "Parallelization method for a continuous property" by P. Pilarczyk was used, 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." 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 in the range [0,499] each. Note that classes of cardinality 1 are not included, as they can be easily determined by verifying which boxes from {0,…,499}✕{0,…,499} are absent in the union of the classes included in the collection. A png file with an illustration of the continuation classes is included in the collection, with each pixel corresponding to a parameter box. Adjacent classes are indicated in different colors, but the colors can be reused for classes that are at some distance from each other. Boxes that belong to classes of cardinality 1 are indicated in white.
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 website http://www.pawelpilarczyk.com/harvesting/.