Chaotic firing in the HR model.

<p>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</p

Bifurcation scenarios observed from different neural pacemakers with decreasing [Ca²⁺]_o.

<p>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.</p

The .

<p>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.</p

The largest Lyapunov exponent.

<p>The largest Lyapunov exponent in parameter space of the HR model (0.0010.035, 2.33.42). Colors shown in the right column are associated with the values of the largest Lyapunov exponent.</p

Spike trains observed from different neural pacemakers.

<p>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.</p

The first return map of the chaotic firing lying between period-1 and period-2 firings.

<p>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.</p

Bifurcation scenarios observed from different neural pacemakers.

<p>(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.</p

Period-6 bursting of isolated neuron when VK2shift = −0.01 V.

<p>(a) Spike trains. The peaks of the 2^nd to 6^th spikes appear at 0.2884 s, 0.4483 s, 0.61s, 0.7761s, 0.9529 s after the cycle, and the 1^st to 6^th troughs appear at 0.233 s, 0.3959 s, 0.5612 s, 0.731 s, 0.9115 s, and 1.2788 s after the cycle; (b) the trajectory of period-6 bursting (thin solid line) in (<i>m</i>_<i>K</i>2, <i>V</i>) plane and fast-slow variable dissection. Upper (UB, dotted line), middle (MB, dashed line), and lower (LB, bold solid line) branches of a Z-shape curve present an unstable equilibrium, saddle, and stable node of the fast subsystem. The intersection pint of MB and LB is a saddle-node (SN) bifurcation point. The upper and lower solid lines correspond to maximum (<i>V</i>_max) and minimum (<i>V</i>_min) values of the stable limit cycle of the fast subsystem. The intersection point of the limit cycle of the fast subsystem and the MB is a saddle-homoclinic (SH) point. Cycle: time delay is zero.</p

The dependence of <i>R</i> on <i>g</i>₁ and <i>g</i>₂ at different <i>τ</i> values.

<p><math><mrow><msubsup><mi>P</mi><mi>l</mi><mi>k</mi></msubsup></mrow></math> (<i>l</i> = 4, 5 or 6, <i>k</i> = 4, 5 or 6) and <math><mrow><msubsup><mi>P</mi><mrow><mi>q</mi><mi>c</mi></mrow><mi>k</mi></msubsup></mrow></math> (<i>k</i> = 6 or 7, “c” represents “b” or “e”) represent synchronous bursting patterns. (a) <i>τ</i> = 0 s; (b) <i>τ</i> = 0.65 s; (c) <i>τ</i> = 0.83 s; (d) <i>τ</i> = 2.3 s; (e) <i>τ</i> = 1.45 s; (f) Enlargement of (e).</p

The response of a pair of negative impulses on a single neuron model.

<p>Burst with 5 spikes (solid line, black) is induced by a pair of negative impulsive currents (dash-and-dot line, blue). Period-6 bursting is shown by thin dashed line (red). (a) <i>A</i> = 0.019 mA and Δ<i>T</i> = 0.133 s. Δ<i>t</i> of the former and latter impulses is 0.61 s (within 4^th spike) and 0.7761 s (within 5^th spike), respectively; (b) Fast/slow dissection corresponding to Fig 4(a). The Z-shape curve presents bifurcation structure of fast-slow dissection to a single neuron model.</p