{"volume":32,"language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Modeling and Simulation"],"issue":"04","page":"713-792","year":"2022","title":"Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision","author":[{"first_name":"N.","full_name":"Bellomo, N.","last_name":"Bellomo"},{"full_name":"Outada, N.","last_name":"Outada","first_name":"N."},{"first_name":"J.","last_name":"Soler","full_name":"Soler, J."},{"full_name":"Tao, Y.","last_name":"Tao","first_name":"Y."},{"full_name":"Winkler, M.","last_name":"Winkler","first_name":"M."}],"type":"journal_article","date_created":"2024-04-07T12:47:28Z","abstract":[{"lang":"eng","text":"<jats:p> 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. </jats:p>"}],"user_id":"31496","doi":"10.1142/s0218202522500166","_id":"53336","status":"public","date_updated":"2024-04-07T12:47:32Z","intvolume":"        32","publisher":"World Scientific Pub Co Pte Ltd","publication_status":"published","publication_identifier":{"issn":["0218-2025","1793-6314"]},"citation":{"bibtex":"@article{Bellomo_Outada_Soler_Tao_Winkler_2022, title={Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision}, volume={32}, DOI={<a href=\"https://doi.org/10.1142/s0218202522500166\">10.1142/s0218202522500166</a>}, number={04}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World Scientific Pub Co Pte Ltd}, author={Bellomo, N. and Outada, N. and Soler, J. and Tao, Y. and Winkler, M.}, year={2022}, pages={713–792} }","ieee":"N. Bellomo, N. Outada, J. Soler, Y. Tao, and M. Winkler, “Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision,” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 32, no. 04, pp. 713–792, 2022, doi: <a href=\"https://doi.org/10.1142/s0218202522500166\">10.1142/s0218202522500166</a>.","chicago":"Bellomo, N., N. Outada, J. Soler, Y. Tao, and M. Winkler. “Chemotaxis and Cross-Diffusion Models in Complex Environments: Models and Analytic Problems toward a Multiscale Vision.” <i>Mathematical Models and Methods in Applied Sciences</i> 32, no. 04 (2022): 713–92. <a href=\"https://doi.org/10.1142/s0218202522500166\">https://doi.org/10.1142/s0218202522500166</a>.","mla":"Bellomo, N., et al. “Chemotaxis and Cross-Diffusion Models in Complex Environments: Models and Analytic Problems toward a Multiscale Vision.” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 32, no. 04, World Scientific Pub Co Pte Ltd, 2022, pp. 713–92, doi:<a href=\"https://doi.org/10.1142/s0218202522500166\">10.1142/s0218202522500166</a>.","ama":"Bellomo N, Outada N, Soler J, Tao Y, Winkler M. Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision. <i>Mathematical Models and Methods in Applied Sciences</i>. 2022;32(04):713-792. doi:<a href=\"https://doi.org/10.1142/s0218202522500166\">10.1142/s0218202522500166</a>","apa":"Bellomo, N., Outada, N., Soler, J., Tao, Y., &#38; Winkler, M. (2022). Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision. <i>Mathematical Models and Methods in Applied Sciences</i>, <i>32</i>(04), 713–792. <a href=\"https://doi.org/10.1142/s0218202522500166\">https://doi.org/10.1142/s0218202522500166</a>","short":"N. Bellomo, N. Outada, J. Soler, Y. Tao, M. Winkler, Mathematical Models and Methods in Applied Sciences 32 (2022) 713–792."},"publication":"Mathematical Models and Methods in Applied Sciences"}