Open AccessChemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision
Author(s) -
Nicola Bellomo,
Nisrine Outada,
Juan Soler,
Youshan Tao,
Michael Winkler
Publication year - 2022
Publication title -
mathematical models and methods in applied sciences/mathematical models and methods in applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.582
H-Index - 85
eISSN - 1793-4060
pISSN - 0218-2025
DOI - 10.1142/s0218202522500166
Subject(s) - computer science , variety (cybernetics) , statistical physics , scale (ratio) , diffusion , focus (optics) , dynamics (music) , nonlinear system , complex system , complex dynamics , artificial intelligence , mathematics , physics , mathematical analysis , quantum mechanics , acoustics , optics , thermodynamics
This paper proposes a review focused on exotic chemotaxis and cross-diffusion models in complex environments. The term exotic is used to denote the dynamics of models interacting with a time-evolving external system and, specifically, models derived with the aim of describing the dynamics of living systems. The presentation first, considers the derivation of phenomenological models of chemotaxis and cross-diffusion models with particular attention on nonlinear characteristics. Then, a variety of exotic models is presented with some hints toward the derivation of new models, by accounting for a critical analysis looking ahead to perspectives. The second part of the paper is devoted to a survey of analytical problems concerning the application of models to the study of real world dynamics. Finally, the focus shifts to research perspectives within the framework of a multiscale vision, where different paths are examined to move from the dynamics at the microscopic scale to collective behaviors at the macroscopic scale.