Entropy Satisfying Schemes for Computing Selection Dynamics in Competitive Interactions
Entropy Satisfying Schemes for Computing Selection Dynamics in Competitive Interactions
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DOI：
10.1137/140965739
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发表时间：
2015-06
期刊：
影响因子：
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通讯作者：
Hailiang Liu;Wenli Cai;N. Su
中科院分区：
文献类型：
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作者：
Hailiang Liu;Wenli Cai;N. Su
在本文中，我们提出了熵满足计划求解的积分微分方程，描述了人口结构的进化相对于一个连续的性状。在[P.- E. Jabin和G.拉乌尔，数学生物学杂志，63（2011），pp. 493- 517]的解收敛到所谓的进化稳定分布（ESD）的时间变得很大，使用相对熵。在离散水平上，ESD被证明是一个二次规划问题的解决方案，可以计算任何成熟的非线性规划算法。然后，该计划满足熵耗散不等式的集合上的初始数据是积极的，数值解往往朝着离散ESD的时间。另一种算法，以捕捉非负的初始数据，这是可能的，由于变异机制内置到修改后的计划的全局ESD。一系列的数值试验，以确认的准确性和熵的满意度。
In this paper, we present entropy satisfying schemes for solving an integro-differential equation that describes the evolution of a population structured with respect to a continuous trait. In [P.-E. Jabin and G. Raoul, J. Math. Biol., 63 (2011), pp. 493--517] solutions are shown to converge toward the so-called evolutionary stable distribution (ESD) as time becomes large, using the relative entropy. At the discrete level, the ESD is shown to be the solution to a quadratic programming problem and can be computed by any well-established nonlinear programing algorithm. The schemes are then shown to satisfy the entropy dissipation inequality on the set where initial data are positive and the numerical solutions tend toward the discrete ESD in time. An alternative algorithm is presented to capture the global ESD for nonnegative initial data, which is made possible due to the mutation mechanism built into the modified scheme. A series of numerical tests are given to confirm both accuracy and the entropy satisf...