4 citations · 4 across the 4 of their papers we have counts for
6 papers
Turing bifurcation, criticality, and multistability in a nonlocal advection-reaction-diffusion equation
Yui Nagayama, Masaharu Nagayama, Hiroshi Ishii
This paper considers a nonlocal advection--reaction--diffusion equation with logistic growth. We investigate how the interaction kernel affects the criticality of Turing bifurcatio…
Global front solutions converging to an asymptotic traveling wave in a time-fractional Amari model
Hiroshi Ishii
We study front propagation in a time-fractional Amari neural field equation with a Caputo derivative and a Heaviside firing-rate function. For a class of nonnegative even connectiv…
Spot solutions to a neural field equation on oblate spheroids
Hiroshi Ishii, Riku Watanabe
Understanding the dynamics of excitation patterns in neural fields is an important topic in neuroscience. Neural field equations are mathematical models that describe the excitatio…
Relationship between haptotaxis and chemotaxis in cell dynamics
Hiroshi Ishii, Hideki Murakawa, Yoshitaro Tanaka
Cell sorting mediated by direct cell--cell contact or cellular protrusions can be described by nonlocal cell--cell adhesion models of haptotaxis type, whereas communication through…
On the approximation of spatial convolutions by PDE systems
Hiroshi Ishii, Yoshitaro Tanaka
This paper develops an approximation framework for spatial convolutions with radial kernels using elliptic PDE systems in arbitrary spatial dimensions. We prove that radial kernels…
Propagating front solutions in a time-fractional Fisher-KPP equation
Hiroshi Ishii
In this paper, we treat the Fisher-KPP equation with a Caputo-type time fractional derivative and discuss the propagation speed of the solution. The equation is a mathematical mode…