A Schematic Bifurcation Diagram with a Normal (Supercritical) Hopf Bifurcation for Illustrating the Transient Resetting Mechanism

<p>A Schematic Bifurcation Diagram with a Normal (Supercritical) Hopf Bifurcation for Illustrating the Transient Resetting Mechanism</p

Synchronization of Two Chaotic Neurons Induced by Common Noise

<p>Synchronization of Two Chaotic Neurons Induced by Common Noise</p

The Relationship between the Duty and the Time Required to Achieve Synchronization in the HH Neuron Model

<p>The Relationship between the Duty and the Time Required to Achieve Synchronization in the HH Neuron Model</p

Robustness of the Mechanism with Parameter Mismatch on <i>G_m</i> in the HH Neuron Model.

<div><p>(A) The relationship between the parameter mismatch Δ<i>G_m</i> and the synchronization error <i>q</i>.</p><p>(B) A typical numerical result of the systems with Δ<i>G_m</i><b> =</b> 0.06.</p></div

Schematic diagram of cortical layers in the early visual cortex (V1/V2).

<p>The bottom-up spike signals via layer 4 from the thalamus core circuit and the top-down spike signals onto layer 1 (and layer 6) interact in the perception of external sensory stimuli in the early cortex (V1/V2). Moreover, acetylcholine (ACh) is transiently released from the nucleus basalis of Meynert to all the layers associated with top-down attention. In layers 2/3, pyramidal neurons (PYRs) that project their apical distal dendrites to layer 1, interneurons (INs), and fast spiking neurons exist. Moreover, it is also known that ACh to layer 1 depolarizes calretinin positive () INs in layer 1 through nicotinic receptors. However, we do not consider the latter effect in our model for simplicity.</p

Robustness of the Mechanism with Parameter Mismatch on <i>I</i>₀ in the HH Neuron Model

<div><p>(A) The relationship between the parameter mismatch Δ<i>I</i> and the synchronization error <i>q</i>.</p><p>(B) A typical numerical result of the systems with Δ<i>I</i><b> =</b> 0.5.</p></div

The dynamics when ACh is gradually decreased according to an exponential function.

<p>In order to simulate more physiologically plausible situations, we evaluated the network dynamics when ACh is decreased according to an exponential function. The top-down Glu spike volleys are injected to the 9th and 10th units for . ACh is also injected at . It is observed that pattern 2 is successfully retrieved while ACh is effective. Therefore, our scenario would hold as well even if the injection of ACh is temporary.</p

Cost versus for (from bottom to top) in homogeneous networks.

<p>(The green dotted vertical line) the theoretical solution ; (the blue short dashed line) the cost of vaccination; (the red dashed lines) the cost of treatment; and (the black solid lines) the total cost. Parameters are set as , , and . The basic per capita cost is set as and the vaccine efficacy is .</p

Comparison of optimal allocations of vaccines in networks with different degree correlations .

<p>(a) and ; (b) and ; (c) and ; (d) and . and the maximal vaccination coverage is . Other parameters are set to the same values as in Fig. 3. Nodes are grouped into 30 groups.</p

Schematic diagram of our model.

<p>(A) As an elemental model of a small network in layers 2/3 in the early visual cortex, we construct a unit model that is composed of PYRs and INs, each of which is modeled as a phase neuron connected to all the other neurons globally. We set and or we take the limit in the analysis of the Fokker-Planck equations (see the <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0053854#s4" target="_blank">Methods</a> section). (B) The multiple units in cortical layers 2/3. ACh decreases inhibitions to PYRs through the presynaptic, muscarinic disinhibitions, and it stabilizes the quasi-attractors. The top-downs Glu spike volleys to the apical distal dendrites of PYRs contribute to the selection of attractors. (C) Connections between two units. Only the connections from the left unit to the right one are shown for simplicity.</p