Spatiotemporal patterns induced by delay and cross‐fractional diffusion in a predator‐prey model describing intraguild predation

Abstract

In this article, we study a reaction-diffusion predator-prey model that describes intraguild predation. We mainly consider the effects of time delay and cross-fractional diffusion on dynamical behavior. By using delay as the bifurcation parameter, we perform a detailed Hopf bifurcation analysis and derive the algorithm for determining the direction and stability of the bifurcating periodic solutions. We also demonstrate that proper cross-fractional diffusion can induce Turing pattern, and the smaller the order of fractional diffusion is, the more easily Turing pattern is able to occur. KEYWORDS cross-fractional diffusion, delay, Hopf bifurcation, predator-prey, Turing pattern MSC CLASSIFICATION 35K57; 35B32; 92D25Math Meth Appl Sci. 2020;43:5179-5196.wileyonlinelibrary.com/journal/mma

Interpretation of entropy generation in Williamson fluid flow with nonlinear thermal radiation and first‐order velocity slip

“…In the last couple of decades, engineers and researchers have been carried out examinations on the important characteristics of fluid flow and heat transfer subject to various assumptions. Combustion problems have been widely studied in a radiated flow towards a stretched and flat surface by numerous analysts 16–29 …”

“…Combustion problems have been widely studied in a radiated flow towards a stretched and flat surface by numerous analysts. [16][17][18][19][20][21][22][23][24][25][26][27][28][29] The present communication, therefore, aims to scrutinize and thus provide awareness on how entropy optimization in radiated flow towards a flat surface of sheet is affected due to variables, that is, magnetic parameter, Darcy-Forchheimer number and radiation parameter, and the type of flow. It is trusted that this would prompt expanded understanding in the current knowledge of heat transport and entropy generation minimization and allow engineers and researchers to design such types of mathematical modeling that not only accomplishes the desired objective in term of heat transport and entropy generation minimization.…”

Dynamical analysis of a delayed diffusive predator–prey model with schooling behaviour and Allee effect

“…In recent years, diffusion has attracted a large attention in the biological models [11,14,37,41]. Since fishes distribute in ocean inhomogeneous in different space at one time t. Thus diffusion should be taken into the model.…”