Continuation classes for a population model with harvesting. Case He-Se: Equal harvesting and equal survival rates of juveniles and adults

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/.本数据集包含基于E. Liz与P. Pilarczyk发表于《理论生物学杂志》第297卷（2012年）第148–165页，DOI为10.1016/j.jtbi.2011.12.012的论文《带收获的阶段结构离散种群模型的全局动力学》中所述研究框架所开展的严谨数值计算的精选结果。 本研究旨在分析恒定收获强度对该论文中所述的、带里克型非线性性（Ricker-type nonlinearity）的幼体-成体阶段结构离散时间种群模型全局动力学的影响。该动力学系统的如下参数被纳入考量：ha、hj分别为成体与幼体的收获率；sa、sj分别为成体与幼体的存活率。 本次研究设置了多种不同情景，每种情景被称为一个特定案例。本数据集对应案例He-Se：幼体与成体的收获率、存活率均相等，即hj=ha，sj=sa，且(ha,sa)∈[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.）第8卷第3期（2009年）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》中所述的通用方案。 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]则以1024×1024的分辨率进行采样。 针对每个参数盒，计算得到了用于围封莫尔斯分解（Morse decomposition）中莫尔斯集的隔离邻域（isolating neighborhoods）集合，并确定了康利-莫尔斯图（Conley-Morse graph）；在可行的前提下，还计算了莫尔斯集的康利指数（Conley index）。同时还计算了相邻参数盒对应的莫尔斯分解之间的粘连图（clutching graphs），并将参数空间划分为若干等价莫尔斯分解类。 本次完整计算基于搭载Debian GNU/Linux系统的四核AMD Opteron™处理器2376 2.3 GHz完成，共耗时1169小时CPU时间，最大内存占用达405 MB。本次计算采用了P. Pilarczyk发表于《计算数学基础》（Foundations of Computational Mathematics）第10卷第1期（2010年）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》中提出的并行化框架。 本数据集包含经计算得到的、可生成等价莫尔斯分解的参数类，这类参数类也被称为延续类（continuation classes）。本数据集仅收录基数至少为2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"*"会被替换为各延续类的序号，序号按类的基数降序排列。每个文件中列出了属于该类的所有参数盒：每个参数盒以括号括起的逗号分隔坐标列表形式定义，文件中每个参数盒单独占一行，其整数坐标的取值范围均为[0,499]。 需注意，本数据集未收录基数为1的延续类，这类类别的参数盒可通过验证集合{0,…,499}×{0,…,499}中未出现在已收录类的并集中的参数盒来便捷确定。 本数据集还包含一张用于展示延续类分布的PNG图像：图像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（距离较远的延续类可复用相同颜色），属于基数为1的类别的参数盒以白色标注。 本系列数据集所包含的全部康利-莫尔斯图与莫尔斯分解相空间相图，均可通过访问网址http://www.pawelpilarczyk.com/harvesting/进行交互式浏览。