Microscopic, kinetic and hydrodynamic hybrid models of collective motions withchemotaxis: a numerical study

• DOI: 10.48550/arxiv.2306.12835
• Publication Date: 2023-01-01
• Authors: Marta Menci; Roberto Natalini; Thierry Paul
• Keywords: Vlasov Equation; Ode; Continuous modelling

A general class of hybrid models has been introduced recently, gathering the advantages multiscale descriptions. Concerning biological applications, particular coupled structure fits to collective cell migrations and pattern formation scenarios. In this context, cells are modelled as discrete entities their dynamics is given by ODEs, while chemical signal influencing motion considered a continuous which solves diffusive equation. From analytical point view, model proved have mean-field limit in Wasserstein distance towards system coupling Vlasov-type equation with chemoattractant Moreover, pressureless nonlocal Euler-type derived for these models, rigorously equivalent Vlasov one monokinetic initial data. present paper, we numerical study solutions Euler systems, exploring settings inital data, far from ones.