The development of a Turing instability to a spatially modulated state in a photoexcited electron-hole system is proposed as a novel signature of exciton Bose statistics. We show that such an instability, driven by kinetics of exciton formation, can result from stimulated processes that build up near quantum degeneracy. The stability of an electron-hole interface which describes recently observ...

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...

The mammalian lung develops through branching morphogenesis. Two primary forms of branching, which occur in order, in the lung have been identified: tip bifurcation and side branching. However, the mechanisms of lung branching morphogenesis remain to be explored. In our previous study, a biological mechanism was presented for lung branching pattern formation through a branching model. Here, we ...

This note investigates the properties of the traveling waves solutions of the nonlocal Fisher equation. The existence of such solutions has been proved recently in [2] but their asymptotic behavior was still unclear. We use here a new numerical approximation of these traveling waves which shows that some traveling waves connect the two homogeneous steady states 0 and 1, which is a striking fact...

Pattern formation in semiconductor heterostructures is studied on the basis of a spatially two{dimensional model of reaction{diiusion type. In particular, we investigate the neighbourhood of a codimension{two Turing{Hopf instability by analytical methods. Amplitude equations are derived which predict the absence of mixed modes but extended ranges of bistability between homogeneous oscillatory s...

Activator-inhibitor systems of reaction-diffusion equations have been used to describe pattern formation in numerous applications in biology, chemistry, and physics. The rate of diffusion in these applications is manifest in the single parameter of the diffusion constant, and stationary Turing patterns occur above a critical value of d representing the ratio of the diffusion constants of the in...

Some quantities in reaction-diffusion models from cellular biology or ecology depend on the spatial average of density functions instead local functions. We show that such nonlocal can induce instability constant steady state, which is different classical Turing instability. For a general scalar equation with average, occurrence state bifurcation rigorously proved, and formula to determine dire...

The reaction–diffusion Holling–Tanner predator–prey model with Neumann boundary condition is considered. We perform a detailed stability and Hopf bifurcation analysis and derive conditions for determining the direction of bifurcation and the stability of the bifurcating periodic solution. For partial differential equation (PDE), we consider the Turing instability of the equilibrium solutions an...