Mathematical analysis and multiscale derivation of a nonlinear predator–prey cross-diffusion–fluid system with two chemicals

Bendahmane, Mostafa; Karami, Fahd; Meskine, Driss; Tagoudjeu, Jacques; Zagour, Mohamed

doi:10.1016/j.cnsns.2024.108090

Communications in Nonlinear Science and Numerical Simulation

2024

DOI: 10.1016/j.cnsns.2024.108090

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Mathematical analysis and multiscale derivation of a nonlinear predator–prey cross-diffusion–fluid system with two chemicals

Mostafa Bendahmane,

Fahd Karami,

Driss Meskine

et al.

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2024

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Multiscale derivation of deterministic and stochastic cross-diffusion models in a fluid: A review

Bendahmane,

Karami,

Zagour

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This paper presents a survey and critical analysis of the mathematical literature on modeling of dynamic populations living in a fluid medium. The present review paper is divided into two main parts: The first part deals with the multiscale derivation of deterministic and stochastic cross-diffusion systems governed by the incompressible Navier–Stokes equations. The derivation is obtained from the underlying description at the microscopic scale in kinetic theory models according to the micro–macro decomposition method. In the second part of this review, we are delighted to present a new variety of mathematical models describing different applications, namely, the pursuit–evasion dynamics, cancer invasion, and virus dynamics. Finally, critical analysis and future research perspectives are discussed.

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Multiscale derivation of deterministic and stochastic cross-diffusion models in a fluid: A review

Bendahmane,

Karami,

Zagour

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

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Mathematical analysis and multiscale derivation of a nonlinear predator–prey cross-diffusion–fluid system with two chemicals

Cited by 1 publication

References 34 publications

Multiscale derivation of deterministic and stochastic cross-diffusion models in a fluid: A review

Multiscale derivation of deterministic and stochastic cross-diffusion models in a fluid: A review

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