Conley-Morse graphs for a population model with harvesting. Case He-S1: Equal harvesting of juveniles and adults, 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 He-S1: Equal harvesting of juveniles and adults, survival rates of juveniles and adults add up to 1, that is: hj = hasj = 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 1,349 hours of CPU time, and the memory usage was up to 780 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 Conley-Morse graphs computed for all the parameter boxes. Each graph is encoded in the text format compatible with the "dot" program from the Graphviz Graph Visualization Software package (https://graphviz.org/). All the text files are compressed together in the zipped archive file. The name of each file is in the format "gn_m.txt", where n,m are the integer coordinates of the box, both in the range [0,499]. For example, in order to obtain a PDF file with the visualizaton of the graph contained in the file "g241_221.txt" one could run the command "dot g241_221.txt -T pdf -o g241_221.pdf". Each node of the graph contains the information on the corresponding isolating neighborhood of a Morse set: the consecutive number of the neighborhood (starting with 0), the number of boxes comprising the neighborhood, and if a Conley index pair was constructed successfully then additionally the homology of the index pair, followed by the index map at each homology level, and the eigenvalues of the map at each homology level. The nodes have different shapes and colors for easy visual identification of the set type; for example, a yellow box indicates an attractor, and a cyan-filled oval stands for an isolating neighborhood with a non-trivial exit set. The directed edges between the nodes show direct connections between the sets (the transitive reduction should be taken for the full set of possible connections). 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《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。
该研究旨在分析恒定努力收获（constant effort harvesting）对该论文中所述带有幼体与成体阶段、具备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。
本次研究考虑的动力学系统参数如下：$h_a, h_j$——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场景，各场景均被称为特定案例。
本数据集收录了案例He-S1的相关数据：幼体与成体收获率相等，幼体与成体存活率之和为1，即：$h_j = h_a$；$s_j = 1 - s_a$；且$(h_a, s_a) in [0,1] imes [0,1]$。
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《A database schema for the analysis of global dynamics of multiparameter systems》中所述的通用方案。
参数空间$[0,1] imes [0,1]$的采样分辨率为$500 imes 500$，相空间$[0,1.35] imes [0,1.35]$的采样分辨率为$1024 imes 1024$。
针对每个参数盒，我们计算了若干包围Morse分解中Morse集（Morse set）的隔离邻域（isolating neighborhood），并构建了Conley-Morse图（Conley-Morse graph），在可行的情况下同步计算Morse集的Conley指数（Conley index）。
同时，我们还计算了相邻参数盒对应的Morse分解之间的粘连图（clutching graphs），并将参数空间划分为等价Morse分解类别。
本次完整计算使用搭载Debian GNU/Linux系统的四核AMD Opteron™ Processor 2376 2.3 GHz处理器完成，总CPU耗时1349小时，最大内存占用达780 MB。
本次计算采用了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《Parallelization method for a continuous property》中提出的并行化框架。
本数据集包含所有参数盒对应的Conley-Morse图。所有图均采用与Graphviz图形可视化软件包中的"dot"程序兼容的文本格式编码。
全部文本文件已打包压缩至单个ZIP归档文件中。
每个文件的命名格式为"gn_m.txt"，其中$n,m$为参数盒的整数坐标，取值范围均为$[0,499]$。
例如，若要将文件"g241_221.txt"中的图形可视化结果导出为PDF文件，可执行命令"dot g241_221.txt -T pdf -o g241_221.pdf"。
每个图的节点包含对应Morse集隔离邻域的相关信息：邻域的连续编号（从0开始）、构成该邻域的参数盒数量；若成功构建了Conley指数对，则额外附上该指数对的同调群信息，以及各同调层级上的指数映射，还有该映射在各同调层级的特征值。
节点采用不同的形状与颜色以便直观识别集合类型：例如，黄色矩形代表吸引子，填充青色的椭圆代表带有非平凡出口集的隔离邻域。
节点间的有向边表示集合之间的直接连接关系（完整的可能连接集需取传递约简）。
本系列数据集提供的全部Conley-Morse图及Morse分解相空间肖像的交互式浏览器可访问网站：http://www.pawelpilarczyk.com/harvesting/。