Meander

Reaction-diffusion equations modeling excitable media are simulated ([6,7]). Initially the spiral rotates periodically about a fixed center. The tip of the spiral (shown in white) traces a circle around the center of rotation. The simulation is then stopped and a model parameter is changed. (Specifically the parameter $a$ which controls the excitability threshold of the system of equations is changed). The spiral now exhibits a more complex motion known as meander. The meander is due to a Hopf bifurcation as seen in the linear stability spectrum.

Model Parameters for simulation:
$$\begin{eqnarray*}& & a=0.70 \rm (periodic) \\& & a=0.60 \rm (meander)\end{eqnarray*}$$
$$\begin{eqnarray*}b=0.01, ~~ \epsilon=0.02, ~~ D_v=0, ~~ L_x=L_y=20.\end{eqnarray*}$$