Paper Info
Title
Entropy Satisfying Schemes for Computing Selection Dynamics in Competitive Interactions
Abstract
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 satisfying property and to underline the efficiency of capturing the large time asymptotic behavior of numerical solutions in various settings.
Year
DOI
Venue
2015
10.1137/140965739
SIAM JOURNAL ON NUMERICAL ANALYSIS
Keywords
Field
DocType
selection dynamics,evolutionary stable distribution,relative entropy,positivity
Mathematical optimization,Entropy rate,Joint quantum entropy,Mathematical analysis,Quantum relative entropy,Binary entropy function,Principle of maximum entropy,Quadratic programming,Mathematics,Kullback–Leibler divergence,Maximum entropy probability distribution
Journal
Volume
Issue
ISSN
53
3
0036-1429
Citations 
PageRank 
References 
0
0.34
4
Authors
3
Name
Order
Citations
PageRank
Hailiang Liu1488.03
wenli cai221.28
Ning Su3233.63