FIGURE 5.

Existence and stability analysis for two bidirectionally pulse coupled oscillators. (A) Firing map for 1:1 phase locking. The two oscillators are labeled as 1 and 2, respectively. Stimulus intervals in a phase locked mode are shown here. The black vertical bars indicate firing times and the gray vertical arrows indicate neuronal inputs at phase ϕ_i (= ts / P_j). P,_i, f_1i and f_2i represent the intrinsic period, the first order resetting and the second order resetting of the i^th oscillator, respectively. (B) Graphical method for determining the fixed points for the firing map given in (A). The intersections of the two curves (black and gray) indicate intervals at which the two periodicity criteria tr₁=g(ts₁) and ts₂=g ⁻¹(tr₂) are satisfied. The circle and the cross symbols indicate the stable and unstable fixed points of the discrete map given in (A).