Abstract Multi-taxis appears in society interactions and cancer treatment. Society can lead to the complex dynamical behavior biology even criminology ([43, 65, 190]).

The present study reports on molecular dynamics investigations of chemically cross-linked poly(ethylene glycol) hydrogels with the aim of exploring the diffusion properties of water, ions, and rhodamine within the polymer at the molecular level. The water structure and diffusion properties were studied at various cross-linking densities with molecular weights of the chains ranging from 572 to 3...

A spatially two-dimensional epidemic model is formulated by a reaction-diffusion system. The spatial pattern formation is driven by a cross-diffusion corresponding to a non-diagonal, uppertriangular diffusion matrix. Whereas the reaction terms describe the local dynamics of susceptible and infected species, the diffusion terms account for the spatial distribution dynamics. For both self-diffusi...

Schnakenberg system is a typical mathematical model to describe activator-depleted kinetics. In this paper, by introducing linear cross-diffusion into system, we derive cross-diffusion-driven Turing instability conditions. It has been revealed that it no longer necessary have long-range inhibition and short-range activation for with the help of cross-diffusion. Then, multiple scales method appl...

This article presents stability analytical results of a two component reaction-diffusion system with linear cross-diffusion posed on continuously evolving domains. First the model system is mapped from a continuously evolving domain to a reference stationary frame resulting in a system of partial differential equations with time-dependent coefficients. Second, by employing appropriately asympto...