Figure 1.
The largest Lyapunov exponent.
The largest Lyapunov exponent in parameter space of the HR model (0.001
0.035, 2.3
3.42). Colors shown in the right column are associated with the values of the largest Lyapunov exponent.
Figure 2.
Bifurcation scenario in the HR model.
Bifurcation scenario of the ISI series dependently with decreasing and increasing
. (A)
; (B)
; (C)
; (D)
.
Figure 3.
Chaotic firing in the HR model.
Chaotic firing lying between period-1 firing and period-2 firing with 2.53 and
0.0245. (A) Spike trains; (B) The first return map of ISI series
Figure 4.
Bifurcation scenarios observed from different neural pacemakers with decreasing [Ca2+]o.
The initial part was from period-1 firing, to chaotic firing, and to period-2 firing. Bifurcation scenario after period-2 firing was different. (A) From chaotic firing, to period-3 firing, to chaotic firing, to period-4 firing. The chaotic firing was divided into 3 parts; (B) A part of Fig. 4(a). Bifurcation scenario from period-1 firing to period-2 firing via chaotic firing; (C) From chaotic firing, to period-3 firing, to chaotic firing, to period-4 firing; (D) From period-4 firing, to chaotic firing, to period-3 firing; (E) From stochastic firing, to period-3 firing, to stochastic firing, to period-4 firing; (F) Period-1 firing.
Figure 5.
Spike trains observed from different neural pacemakers.
Spike trains of the chaotic firing lying between period-1 and period-2 firings. (A) Part 1 of the first example; (B) Part 2 of the first example; (C) Part 3 of the first example; (D) The second example; (E) The third example; (F) The fourth example; (G) The fifth example.
Figure 6.
The first return map of the chaotic firing lying between period-1 and period-2 firings.
The first return map of ISI series observed from different neural pacemakers. (A) Part 1 of the first example; (B) Part 2 of the first example; (C) Part 3 of the first example; (D) The second example; (E) The third example; (F) The fourth example; (G) The fifth example.
Figure 7.
The of chaotic firings lying between period-1 and period-2 firings observed from different neural pacemakers. Line with triangle, original data; line with circle, mean of 10 realizations of surrogate data. (A) Part 1 of the first example; (B) Part 2 of the first example; (C) Part 3 of the first example; (D) The second example; (E) The third example; (F) The fourth example; (G) The fifth example.
Figure 8.
Bifurcation scenarios observed from different neural pacemakers.
(A) Inverse bifurcation scenario corresponding to Fig. 4(D) with increasing [Ca2+]o from 0 mM to 1.2 mM, whose process was from period-3 firing, to chaotic firing, to period-4 firing, to period-2 firing, to chaotic firing, and to period-1 firing; (B) Inverse bifurcation scenario corresponding to Fig. 4(E) with increasing [Ca2+]o from 0 mM to 1.2 mM, whose process was from period-4 firing, to stochastic firing, to period-3 firing, to stochastic firing, to period-2 firing, to chaotic firing, and to period-1 firing; (C) Bifurcation scenario observed in a neural pacemaker with decreasing [Ca2+]o from 1.2 mM to 0 mM, whose process was from period-1 firing to period-2 firing via chaotic firing, to chaotic firing, to period-3 firing, and to chaotic firing; (D) Inverse bifurcation scenario corresponding to Fig. 8(C) with increasing [Ca2+]o from 0 mM to 1.2 mM, whose process was from chaotic firing, to period-3 firing, to chaotic firing, to period-2 firing, to chaotic firing, and to period-1 firing.