Fig. 2

Convergence of pairwise level crossing correlations. a Spike correlation function ${\nu }_{\mathrm{cond}}(\tau )$ vs. time lag τ for different truncation orders n in Eq. (17); $r=0.7$, ${\sigma }_{V_1}={\sigma }_{V_2}=10\text{ mV}$, ${\tau }_s=\text{20 ms}$, $\nu =5\text{ Hz}$, $\psi =9.64\text{ mV}$. b${\nu }_{\mathrm{cond}}(\tau )$ vs. τ for a pair of rate heterogeneous neurons with $r=0.7$, ${\sigma }_{V_1}=10\text{ mV}$, ${\sigma }_{V_2}=5\text{ mV}$, ${\tau }_s=20\text{ ms}$, ${\nu }_1=5\text{ Hz}$, ${\nu }_2=1.24\text{ Hz}$, $\psi =9.64\text{ mV}$. c${\nu }_{\mathrm{cond}}(\tau )$ vs. time lag for varying correlation strengths r in a pair of neurons with ${\sigma }_{V_1}={\sigma }_{V_2}=10\text{ mV}$, ${\tau }_s=20\text{ ms}$, $\nu =5\text{ Hz}$, $\psi =9.64$. d${\nu }_{\mathrm{cond}}(\tau )$ vs. time lag for varying correlation strengths r, in a pair of rate heterogeneous neurons with ${\sigma }_{V_1}=10\text{ mV}$, ${\sigma }_{V_2}=5\text{ mV}$, ${\tau }_s=20\text{ ms}$, ${\nu }_1=5\text{ Hz}$, ${\nu }_2=1.24\text{ Hz}$, $\psi =9.64$. The truncation order of ${\nu }_{\mathrm{cond}}(\tau )$-series in Eq. (17) in c–d is $n=10$. In a–d the filled circles at $\tau =0$ indicate the predicted ${\nu }_{\mathrm{cond}}(0)$ (as in Eq. (23)) and colored squares denote the corresponding numerical simulations obtained with $N=2000$ independent realizations of 20 s length