Phase transition diagrams of the spiking patterns generated by the Hodgkin-Huxley model with power-law behaving conductances.

<p>The power-law dynamics was implemented with a fractional order derivative of order <i>η</i> for the respective gating variables. (A) Potassium conductance activation n gate. (B) Sodium conductance activation m gate. (C) Sodium conductance inactivation h gate. RS, resting state; PS, phasic spiking; MMO, mixed-mode oscillations; TS, tonic spiking; SWB, square-wave bursting; and PPB, pseudo-plateau bursting. Spiking responses and boundaries were manually classified based on the first 1,500 ms of simulation.</p

Phase plane plots of the square wave bursting and the two types of pseudo plateau potential spiking patterns in the Hodgkin-Huxley model with power-law behaving h gate.

<p>Same settings as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004776#pcbi.1004776.g008" target="_blank">Fig 8</a>. (A) Phase plot of the sodium (I_na) vs I_w = potassium + leak + injected currents, the red square shows the place of the attractor. (B) The attractors from A plotting balanced current (I_na+I_w) vs I_w.</p

Phase plane analysis of the Transient Spiking pattern (see Fig 4B).

<p>(A) Comparison of the current trajectories of the power-law (black) and classic (gray) Hodgkin-Huxley model. The power-law model had a fractional order derivative of <i>η</i> = 0.4 and input current I = 8 nA. The red box indicates the area of the attractor. (B) Phase plane of the attractor in A. S1 to S4 indicate spikes and RS is the resting state.</p

Action potential patterns generated by a Hodgkin-Huxley model modified with power-law behaving n (A-C) and h (D-F) gates.

<p>Each panel has the information of the current input (I) and value used for the respective fractional order derivative (<i>η</i>).</p

The contribution of the memory trace to Mixed Mode Oscillations in the Hodgkin-Huxley model with power-law n gate.

<p>The power-law dynamics was implemented with fractional derivative of order <i>η</i> = 0.7 and constant input current I = 23 nA. (A-E) Examples over a long (left) and short (right) time window of the voltage, memory trace, and gate values. The gray line is the identical simulation with <i>η</i> = 1.0. (F-H) Phase plane analysis of the same responses. (F) Phase plot of the sodium (I_Na) vs I_w = potassium + leak + injected currents. The red line indicates the balance current and the red square indicates the presence of an attractor. (G) Zoom in the attractor in F. (H) Same data as in G but plotting the imbalance current (I_Na+I_w) vs I_w. The * indicates where I_w starts compensating for I_Na.</p

Action potential spiking patterns due to power-law conductances in response to constant current input.

<p>(A-D) Spiking patterns generated with power-law behaving n gate. (E-G) Spiking patterns generated with power-law behaving h gate. Each set of simulations done with identical input current and varying the order of the fractional derivative (<i>η</i>).</p