Continuation classes for a population model with harvesting. Case Ha-S1: Harvesting adults only, survival rates of juveniles and adults add up to 1

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 Ha–S1: Harvesting adults only, survival rates of juveniles and adults add up to 1, that is: hj = 0sj = 1 – 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 2,929 hours of CPU time, and the memory usage was up to 1,767 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/.本数据集包含由E. Liz与P. Pilarczyk发表于《理论生物学杂志（Journal of Theoretical Biology）》2012年第297卷第148–165页、DOI: 10.1016/j.jtbi.2011.12.012的论文《Global dynamics in a stage-structured discrete population model with harvesting》中所述研究框架内开展的严谨数值计算的精选结果。 本研究旨在分析恒定努力收获对文中所述带有幼体与成体阶段、具备里克型（Ricker-type）非线性项的离散时间种群模型全局动力学的影响。本研究考量了该动力系统的如下参数：$h_a, h_j$ 分别为成体与幼体的收获率；$s_a, s_j$ 分别为成体与幼体的存活率。本次研究设置了若干不同情景，各情景被称为特定案例。 本数据集对应案例Ha–S1：仅对成体实施收获，幼体与成体的存活率满足 $s_a + s_j = 1$，即 $h_j = 0$，且参数对 $(h_a, s_a) in [0,1] imes [0,1]$。 本次计算遵循Z. Arai、W. Kalies、H. Kokubu、K. Mischaikow、H. Oka与P. Pilarczyk发表于《SIAM应用动力系统期刊（SIAM J. Appl. Dyn. Syst.）》2009年第8卷第3期第757–789页、DOI: 10.1137/080734935的论文《A database schema for the analysis of global dynamics of multiparameter systems》中所述的通用方案。 本次计算对参数空间 $[0,1] imes [0,1]$ 以500×500的分辨率进行采样，对相空间 $[0,1.35] imes [0,1.35]$ 以1024×1024的分辨率进行采样。针对每个参数盒，计算了用于包围莫尔斯分解（Morse decomposition）中莫尔斯集（Morse set）的隔离邻域集合，并确定了康利-莫尔斯图（Conley-Morse graph），同时在可行条件下计算了莫尔斯集的康利指数（Conley index）。此外，还计算了相邻参数盒对应的莫尔斯分解之间的连接图（clutching graph），并将参数空间划分为等价莫尔斯分解类。 本数据集的完整计算在搭载Debian GNU/Linux系统的四核AMD Opteron™处理器2376 2.3 GHz设备上完成，总CPU时长为2929小时，最大内存占用达1767 MB。本次计算使用了P. Pilarczyk发表于《计算数学基础（Foundations of Computational Mathematics）》2010年第10卷第1期第93–114页、DOI: 10.1007/s10208-009-9050-8的论文《Parallelization method for a continuous property》中提出的并行化框架。 本数据集包含计算得到的、可产生等价莫尔斯分解的参数类，该类亦被称为“延续类（continuation class）”。本数据集仅提供包含至少2个参数盒的延续类。每个延续类均存储于名为`cont*.cub`的文本文件中，其中`*`替换为各延续类的序号，序号按类的基数降序排列。每个文件包含所属延续类的参数盒列表，每个参数盒以逗号分隔的坐标列表形式定义，并以括号包裹。文件中每个参数盒单独占一行，其整数坐标范围均为 $[0,499]$。 需注意，本数据集未包含基数为1的延续类，此类可通过验证${0,dots,499} imes {0,dots,499}$中未出现在已收录延续类并集内的参数盒来便捷获取。 本数据集集合中还包含一张用于展示延续类的PNG图片，其中每个像素对应一个参数盒。相邻的延续类以不同颜色区分，但对于彼此间距较远的延续类，可重复使用相同颜色。属于基数为1的延续类的参数盒以白色标记。 本系列数据集所提供的所有康利-莫尔斯图及莫尔斯分解的相空间轨图的交互式浏览器，可通过网址http://www.pawelpilarczyk.com/harvesting/ 访问。