Continuation classes for a population model with harvesting. Case Hj-S1: Harvesting juveniles 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 Hj-S1: Harvesting juveniles only, survival rates of juveniles and adults add up to 1, that is: ha = 0sj = 1 – sa(hj,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 1,410 hours of CPU time, and the memory usage was up to 607 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/.

本数据集收录了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为10.1016/j.jtbi.2011.12.012的论文《阶段结构带收获的离散种群模型全局动力学（Global dynamics in a stage-structured discrete population model with harvesting）》中所述研究的严谨数值计算精选结果。
本研究旨在分析恒定努力收获对该论文中提出的带有幼体、成体阶段且具有Ricker型非线性（Ricker-type nonlinearity）的离散时间种群模型全局动力学的影响。本次研究考量了多种不同场景，每种场景被称为特定案例。
当前数据集对应案例Hj-S1：仅对幼体实施收获，且幼体与成体的存活率之和为1，即h_a = 0，s_j = 1 - s_a，其中(h_j, s_a) ∈ [0,1]×[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应用动力系统杂志（SIAM J. Appl. Dyn. Syst.）》2009年第8卷第3期第757–789页、DOI为10.1137/080734935的论文《多参数系统全局动力学分析的数据库框架（A database schema for the analysis of global dynamics of multiparameter systems）》中所述的通用流程。
参数空间[0,1]×[0,1]以500×500的分辨率进行采样，相空间[0,1.35]×[0,1.35]以1024×1024的分辨率进行采样。针对每个参数格点，计算了包围Morse分解（Morse decomposition）中Morse集（Morse set）的隔离邻域（isolating neighborhood）集合，并确定了Conley-Morse图（Conley-Morse graph），在可行情况下计算了各Morse集的Conley指数（Conley index）。
同时计算了相邻参数格点对应的Morse分解之间的粘连图（clutching graph），并将参数空间划分为等价Morse分解类。
本次完整计算在搭载Debian GNU/Linux系统的四核AMD Opteron™ Processor 2376 2.3 GHz处理器上完成，总CPU耗时1410小时，最大内存占用达607 MB。
计算采用了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为10.1007/s10208-009-9050-8的论文《连续性质的并行化方法（Parallelization method for a continuous property）》中提出的并行计算框架。
本数据集包含计算得到的等价Morse分解参数类，亦称为"延续类（continuation class）"。仅收录基数至少为2的类。
每个延续类以文本文件"cont*.cub"存储，其中"*"替换为按类基数降序排列的类序号。
每个文件包含所属类的参数格点列表，每个格点以逗号分隔的坐标列表表示，并以括号括起，文件中每行对应一个格点。格点的整数坐标取值范围均为[0,499]。
未收录基数为1的类，因为可通过验证{0,…,499}×{0,…,499}中未出现在已收录类并集中的格点，轻松得到此类。
数据集还包含一张展示延续类的PNG（Portable Network Graphics）图片，图片中每个像素对应一个参数格点。相邻类以不同颜色区分，颜色可重复用于间距较远的类，基数为1的类对应的格点以白色标示。
本系列数据集附带的所有Conley-Morse图及Morse分解相空间肖像的交互式浏览器，可通过网址http://www.pawelpilarczyk.com/harvesting/ 访问。