Cross-diffusion on multiplex networks

Abstract

During the past decades, pattern formulation with reaction-diffusion systems has attracted great research interest. Complex networks, from single-layer networks to more complicated multiplex networks, have made great contribution to the development of this area, especially with emergence of Turing patterns. While among vast majority of existing works on multiplex networks, they only take into account the simple case with ordinary diffusion, which is termed as self-diffusion. However, cross-diffusion, as a significant phenomenon, reveals the direction of species' movement, and is widely found in chemical, biological and physical systems. Therefore, we study the pattern formulation on multiplex networks with the presence of both self-diffusion and cross-diffusion. Of particular interest, heterogeneous patterns with abundant characteristics are generated, which cannot arise in other systems. Through linear analysis, we theoretically derive the Turing instabilities region. Besides, our numerical experiments also generate diverse patterns, which verify the theoretical prediction in our work and show the impact of cross-diffusion on pattern formulation on multiplex networks.

Patterns in the predator–prey system with network connection and harvesting policy

“…For the Turing instability, we find that the connecting probability of the nodes plays an important role in pattern formation, see Figures 6–10. This is different from the case of the system without network structure and this finding does not appeared in many existing literature, see previous studies 12–23 . Hence, the obtained results are rich and interesting.…”

“…This is different from the case of the system without network structure and this finding does not appeared in many existing literature, see previous studies. [12][13][14][15][16][17][18][19][20][21][22][23] Hence, the obtained results are rich and interesting. For more complex and interesting dynamical behaviors, for example, the Turing-Hopf bifurcation, of this model will be further considered.…”

“…In this present paper, unlike the existing literature mentioned before, for instance, previous studies, 12–23 we establish the amplitude equations of the Hopf bifurcation by MTS. As such, the supercritical or the subcritical Hopf bifurcation can be determined.…”

“…Liu et al 16 showed that discrete Laplacian diffusion induced different spreading speeds in different invasive directions, utilizing a two-species competition model with the network. For more results about reaction-diffusion models with network connection, please refer to previous studies [17][18][19][20][21][22][23][24] and references cited therein. Therefore, inspired by these previous works, we build a network connection with respect to the reaction-diffusion predator-prey model (2) with the number of its nodes N and suppose that each node has no self-loop on this network.…”

Coupled disease-vaccination behavior dynamic analysis and its application in COVID-19 pandemic

“…For example, Zhu et al proposed a two-layer network model to study the spreading properties of lethal diseases [32] . Gao et al introduced a model on multiplex networks with the presence of self-diffusion and cross-diffusion [33] .…”