Hopf bifurcation analysis in the 1-D Lengyel-Epstein reaction-diffusion model
The authors have investigated the rich by Turing instability and bifurcation phenomena dynamics of the Neumann problem for the Lengyel-Epstein reaction-diffusion system \[ \left.\begin{aligned} &u_t=\Delta u+a-u-\frac{4uv}{1+u^2}\\ &v_t=c\Delta v+b\left(u-\frac{uv}{1+u^2}\right)\end{aligned}\right\} \quad x\in\Omega, \] \[ \frac{\partial u}{\partial \nu}=\frac{\partial v}{\partial \nu}=0,\qquad x\in\partial\Omega, \qquad \qquad \] (\(\Omega\) is a bounded domain with sufficiently smooth boundary \(\partial\Omega\), \(a\), \(b\) and \(c\) are positive constants) with the aim to find spatially non-homogeneous periodic solutions, i.e., periodic solutions caused by diffusion.
scientific article; zbMATH DE number 5687651