Over the past two decades, molecular and cell biologists have made important progress in
characterizing the components and compartments of the cell. New visualization methods …

In this paper, we investigate the spatial pattern formation of a predator–prey system with
prey-dependent functional response Ivlev-type and reaction-diffusion. The Hopf bifurcation …

Spatially periodic, temporally stationary patterns that emerge from instability of a
homogeneous steady state were proposed by Alan Turing in 1952 as a mechanism for …

In this book we consider solution branches and bifurcations in nonlinear partial differential
equations (PDEs) as models from science (and some economics). Given a nonlinear PDE …

This study demonstrates computational simulations of multicellular deformation coupled with
chemical patterning in the three-dimensional (3D) space. To address these aspects, we …

The study of pattern-forming instabilities in reaction–diffusion systems on growing or
otherwise time-dependent domains arises in a variety of settings, including applications in …

Tooth development is governed largely by epithelial–mesenchymal interactions and is
mediated by numerous signaling pathways. This type of morphogenetic processes has been …

This book examines how to program artificial search agents so that they act optimally or
demonstrate the same behavior as predicted by the foraging theory for living organisms. It …

The formation of ordered structures, in particular Turing patterns, in complex spatially
extended systems has been observed in many different contexts, spanning from natural …

In this paper, we research the pattern dynamics in a spatial fractional Leslie–Gower predator–
prey model with fear effect and refuge. The comprehensive effects of these factors on system …