Isaac Klapper, Daniel B. Szyld, Xinli Yu, Karsten Zengler, Tianyu Zhang, Cristal Zúñiga
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引用次数: 0
Abstract
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 97-113, February 2024. Abstract. Microbes are able to deploy different strategies in response to, and depending upon, local environmental conditions. In the setting of a microbial community, this property induces a Nash equilibrium problem because access to environmental resources is bounded. If microbes are also distributed in space, then those resources are subject to transport limitations (encoded in a PDE) and so microbial strategies at one location influence resources and, hence, microbial strategies, at another. Here we formulate the resulting PDE-coupled generalized Nash equilibrium problem for a multispecies biofilm community, and propose a domain-decomposition-based method for its solution. An example consisting of a model with two microbial species biofilm with 33 externally transported chemical concentrations is presented.
期刊介绍：
SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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