= Three-region calcium nullcline
{title2=$J(u)-K(u)v^2/(1+v^2)-\delta v=0$}
For $J=\beta u^2/(1+u^2)$ and $K=u^4/(1+u^4)$ with small leak $\delta$, the positive <nullcline> is unique at each $u$ because its <derivative> with respect to $v$ is strictly negative. Its asymptotic regions are a high-store balance $v\simeq(J-K)/\delta$, a crossing balance near $J(u_c)=K(u_c)$, and a negligible-leak balance $v^2/(1+v^2)\simeq J/K$. The crossing relation is $(K_c'-J_c')(u-u_c)\simeq K_c/v^2-\delta v$. These describe one continuous curve, not three distinct equilibria at a fixed cytoplasmic <concentration>.
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