共查询到17条相似文献,搜索用时 62 毫秒
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Gompertz模型和Logistic模型的拟合 总被引:15,自引:1,他引:14
朱珉仁 《数学的实践与认识》2002,32(5):705-709
常见的三参数 S形生长模型有 Gompertz模型和 L ogistic模型 .它们在拐点处的坐标、导数与它们的参数是能够相互唯一确定的 .当利用拟事隐函数曲线的 GNL 法对这两种模型进行最小二乘拟合时 ,可根据这一性质对单个未线性化参数的初始值进行搜索 .有时也可对该初始值直接进行搜索 .最后以几个实例成功地对这种算法进行了验证 相似文献
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本文研究一类具有分段常数变量的三维食饵-捕食者系统的稳定性和分支行为,该系统由一个捕食者和两个食饵构成,其中一个食饵可由捕食者对另一个食饵的捕食行为中获益.首先通过计算得到三维食饵-捕食者系统对应的差分模型,其次通过选择合适的参数讨论边界和正平衡点的存在性,进而利用线性稳定性理论讨论平衡点局部渐近稳定的充分条件.将两个食饵种群的出生率以及最大环境容纳量作为分支参数,使用分支理论研究差分模型在平衡点处产生翻转分支、Neimark-Sacker分支、折-翻转分支和1:2共振分支的充分条件.最后通过数值模拟验证了理论分析的正确性. 相似文献
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研究了同一鱼类种群同时分布于保护区斑块和非保护区斑块,且鱼群密度服从Gompertz增长的生物经济系统.首先,证明了系统内存在唯一的非平凡奇点并且局部稳定,运用Bendixson-Dulac定理得到该奇点的全局稳定性;然后,通过Pontryagin最大值原理获得该鱼类种群的最优捕捞路径;最后,通过数值模拟来说明部分结论. 相似文献
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《数学的实践与认识》2019,(24)
讨论了一类带有避难所的捕食-食饵模型的稳定性和Neimark-Sacker分支行为.首先通过计算得到该模型对应的差分方程,利用线性稳定性理论讨论平衡点的局部渐近稳定性;其次运用正规形理论和中心流形投影法阐释了系统随参数变化而发生翻转分支和Neimark-Sacker分支进入混沌的情形;最后进行数值模拟验证研究理论结果的正确性. 相似文献
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本文研究一类带有疾病和分段常数变量的捕食-被捕食模型的稳定性和分支行为.首先通过计算得到捕食-被捕食模型对应的差分模型,利用线性稳定性理论讨论边界和正平衡点局部渐近稳定的充分条件.其次将食饵种群的出生率作为分支参数,使用分支理论研究差分模型在边界和正平衡点处产生鞍结点分支、翻转分支、Neimark-Sacker分支、Neimark-Sacker分支、鞍结点-Neimark-Sacker分支、鞍结点-翻转分支和翻转-Neimark-Sacker分支的充分条件.最后数值模拟验证理论分析的正确性,并展示模型复杂的动力学性态. 相似文献
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王烈 《高校应用数学学报(A辑)》2014,29(4)
研究一类带有分段常数变量和避难所的天敌-害虫模型的稳定性和分支行为.首先通过计算转化得到天敌-害虫模型对应的差分模型,利用线性稳定性理论讨论了正平衡态局部渐近稳定的充分条件.其次以害虫种群的内禀增长率或逃脱率为分支参数,利用分支理论研究了模型正平衡态处产生翻转分支周期解和Neimark-Sacker分支周期解的充分条件;并且使用正规形理论和中心流形定理构造了判断分支周期解稳定性的阈值.最后数值模拟验证了理论分析的正确性,并展示了该模型复杂的动力学行为. 相似文献
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Gompertz模型在高龄阶段的修正及模拟 总被引:1,自引:0,他引:1
近年来我国人口老龄化呈加快之势 ,精确估计高龄老人的年龄别死亡概率对人寿保险公司计算年金显得尤为重要 .本文针对观察年龄别死亡概率在高龄阶段不再呈现指数增长的事实 ,对 Gompertz模型进行了修正 ,以使模型更好地拟合观察年龄别死亡概率 . 相似文献
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Logistic阻滞增长模型的稳定性与混沌 总被引:3,自引:0,他引:3
将Logistic阻滞增长模型的差分形式简化,讨论了它的稳定性,用计算机进行迭代求解。模拟了这一简单差分方程从收敛,分叉,2^n倍周期收敛进入混沌现象的过程。直观地展示了序列{yk}收敛,2倍周期,4倍周期……直至混沌的现象,这对Logistic阻滞增长模型的应用和混沌现象的模拟有很好的参考价值。 相似文献
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Global stability of a delayed ratio-dependent predator-prey model with Gompertz growth for prey
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A delayed ratio-dependent predator-prey model with Gompertz growth for prey is investigated. The local stability of a predator-extinction equilibrium and a coexistence equilibrium is discussed. Furthermore, the existence of Hopf bifurcation at the coexistence equilibrium is established. By constructing a Lyapunov functional, sufficient conditions are obtained for the global stability of the coexistence equilibrium. 相似文献
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Yumei Yu Wendi Wang Zhengyi Lu 《Journal of Mathematical Analysis and Applications》2007,334(1):333-348
The model of three competitive populations with Gompertz growth is studied. The periodic solutions are ruled out by generalized Dulac criteria. On the basis of the analysis, we obtain conditions that ensure the asymptotic behavior of the model is simple. 相似文献
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Janaina S. B. Toledo Vera Lucia D. Tomazella Cleide Mayra M. Lima Matheus H. Felix 《商业与工业应用随机模型》2023,39(2):177-197
In the financial market, it is important to consider that there is a proportion of customers that have settled their debt in time zero, immediately recovering their ability to pay. In this context, in this paper, we propose a survival analysis methodology that allows the insertion of times equal to zero in scenarios where credit risk is observed. The proposed model addresses the survival analysis model of the zero-inflated cure rate which incorporates the heterogeneity of three subgroups (individuals having events in the initial time, and individuals not susceptible and susceptible to the event). In our proposal, all available survival data of customers are modeled considering that the number of competitive causes follows a Poisson distribution and the baseline risk function follows a Gompertz distribution. The model parameter estimation is obtained by the maximum likelihood estimation procedure and simulation studies are conducted to evaluate the estimators' performance. The studied methodology will be applied to a credit database provided by a financial institution in Brazil. 相似文献
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We propose a new model – we call it a smoothed threshold life table (STLT) model – to generate life tables incorporating information on advanced ages. Our method allows a smooth mortality transition from non-extreme to extreme ages, and provides objectively determined highest attained ages with which to close the life table.We proceed by modifying the threshold life table (TLT) model developed by Li et al. (2008). In the TLT model, extreme value theory (EVT) is used to make optimal use of the relatively small number of observations at high ages, while the traditional Gompertz distribution is assumed for earlier ages. Our novel contribution is to constrain the hazard function of the two-part lifetime distribution to be continuous at the changeover point between the Gompertz and EVT models. This simple but far-reaching modification not only guarantees a smooth transition from non-extreme to extreme ages, but also provides a better and more robust fit than the TLT model when applied to a high quality Netherlands dataset. We show that the STLT model also compares favourably with other existing methods, including the Gompertz–Makeham model, logistic models, Heligman–Pollard model and Coale–Kisker method, and that a further generalisation, a time-dependent dynamic smooth threshold life table (DSTLT) model, generally has superior in-sample fitting as well as better out-of-sample forecasting performance, compared, for example, with the Cairns et al. (2006) model. 相似文献
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运用微分方程稳定性理论,建立了在砍伐情况下林场树木量遵从的方程,分析了树木量稳定的条件,并且在稳定的前提下讨论如何控制砍伐使持续产量和经济效益达到最大.最后研究了砍伐过度的问题. 相似文献