Fig 1.
System behavior in case of regular spiking (RS).
(a) Time evolution of v(t). (b) Typical trajectory, including state-dependent jump, in the (v, u) phase plane (a = 0.02, b = 0.2, c = −65, d = 8, I = 10 [3]).
Fig 2.
Chaotic system behavior for d = −16.
(a) Time evolution of v(t). (b) Its trajectory in the (v, u) phase plane. The dashed line represents the v-nullcline (v′ = 0) and the dotted line represents the u-nullcline (u′ = 0). The arrows indicate the vector field of v and u. (c) The return map of (ui, ui + 1), where the solid line represents the orbit of ui, the dotted line represents the solution of ui + 1 = ψ(ui), and the dashed line depicts ui + 1 = ui. (a = 0.2, b = 2, c = −56, I = −99, d = −16).
Fig 3.
Dependence of Lyapunov exponents λj (j = 1, 2) on the input DC current I (a = 0.2, b = 2, c = −56, d = −16).
Fig 4.
Dependence of bifurcation on parameter d.
(a) Bifurcation diagram of ui. (b) Lyapunov exponents λj (j = 1, 2). (c) Coefficient of variation for inter-spike interval CV (a = 0.2, b = 2, c = −56, I = −99).
Fig 5.
Time series of membrane potential v(t) (left) and attractor (right).
(a) d = −11, (b) d = −12, (c) d = −13, (d) d = −16 (a = 0.2, b = 2, c = −56, I = −99).
Fig 6.
System behavior at the Poincaré section. Time series of ui (left). Return map of (ui, ui + 2) (right).
The solid line represents the orbit of ui, the dotted line shows the solution to ui + 2 = ψ2(ui), and the dashed line depicts ui + 2 = ui. (a) d = −11, (b) d = −12, (c) d = −13, (d) d = −16 (a = 0.2, b = 2, c = −56, I = −99).
Fig 7.
Dependence of bifurcation on parameter d under weak sinusoidal signal.
(a) Bifurcation diagram of ui.(b) Lyapunov exponents λj (j = 1, 2). (c) Coefficient of variation for inter-spike interval CV. (a = 0.2, b = 2, c = −56, I = −99, A = 0.3, f0 = 0.1).
Fig 8.
Cycle histogram (top) and time series of v(t) (bottom).
In cases of (a) chaotic firing (d = −16) and (b) periodic firing (d = −10). is a histogram of firing counts at tk mod (T0) (k = 1, 2, ⋯). The dotted lines are the input signals
(a = 0.2, b = 2, c = −56, I = −99, A = 0.3, f0 = 1/T0 = 0.1).
Fig 9.
Dependence of spike timing on signal strength A in periodic state.
(a) Mean of inter spike interval < Tk >. (b) Spike timing against input signal. (a = 0.2, b = 2, c = −56, d = −10, I = −99, f0 = 0.1).
Fig 10.
Dependence of signal response on parameter d in CR.
(a) d dependence of maxτ C(τ) between cycle histogram and input signal
. The upper part of this figure shows the time delay ∣τ∣, i.e., these values realize the maximum value of C(τ). (b) d dependence of MI(F; S) between cycle histogram
and input signal
. (a = 0.2, b = 2, c = −56, I = −99, A = 0.3, f0 = 0.1).
Fig 11.
Dependence of maxτ C(τ) on parameter d and signal strength A.
The dotted red line represents the d-threshold of λ1 > 0 (dthr) at each value of signal strength A (a = 0.2, b = 2, c = −56, I = −99, f0 = 0.1).
Fig 12.
Dependence of bifurcation and signal response on parameter d in CR.
Under the condition of weaker signals (A = 0.01) than those shown in Figs 7 and 10. (a) Bifurcation diagram of ui. (b) λj. (c) CV.(d) maxτ C(τ). (Upper part indicates time delay ∣τ∣). (e) MI(F; S) (a = 0.2, b = 2, c = −56, I = −99, f0 = 0.1).
Fig 13.
Scatter plot of maxτ C(τ) and λ1 in region −13.5 ≤ d ≤ −11 from Fig 12.
The red dotted line indicates the mean value of maxτ C(τ) in bin λ1 with window Δλ1 = 0.001.
Fig 14.
Dependence of signal response on signal frequency f0.
(a) maxτ C(τ). (b) MI(F; S). (c) λj. (a = 0.2, b = 2, c = −56, I = −99, d = −12.19, A = 0.01).