Aliev

For the Aliev model,

$$F(v,w) = g_a(v-\beta)(v-\alpha)(1-v) - vw$$ (12)

$$G(v,w) = - \epsilon(v,w)( w + g_s(v-\beta)(v-\alpha-1)$$ (13)

where $\epsilon(v,w) = \epsilon_1+ \mu_1{w\over v+\mu_2}$.

Reasonable parameter values are $\beta= 0.0001$ , $\alpha = 0.05$, $g_a = 8.0$, $g_s = 8.0$, $\mu_1 = 0.05$, $\mu_2 = 0.3$, $\epsilon_1 = 0.03$, $\epsilon_2 = 0.0001$. Parameter values that give spiral breakup are $\alpha = 0.1$, $g_a = 8.0$, $g_s = 8.0$, $\mu_1=0.07$, $\mu_2 = 0.3$, and $\epsilon_1 = 0.01$.