By Wulfram Gerstner
This creation to spiking neurons can be utilized in advanced-level classes in computational neuroscience, theoretical biology, neural modeling, biophysics, or neural networks. It makes a speciality of phenomenological techniques instead of distinctive versions that allows you to give you the reader with a conceptual framework. The authors formulate the theoretical suggestions truly with out many mathematical information. whereas the ebook comprises average fabric for classes in computational neuroscience, neural modeling, or neural networks, it additionally offers an access to present learn. No earlier wisdom past undergraduate arithmetic is needed.
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Extra resources for Spiking neuron models: single neurons, populations, plasticity
Thus, if some external input causes the membrane voltage to rise, the conductance of sodium channels increases due to increasing m. As a result, positive sodium ions flow into the cell and raise the membrane potential even further. If this positive feedback is large enough, an action potential is initiated. 4: A. Action potential. The Hodgkin-Huxley model has been stimulated by a short, but strong, current pulse before t = 0. The time course of the membrane u(t) = u(t) - urest for t > 0 shows the action potential (positive peak) potential followed by a relative refractory period where the potential is below the resting potential.
9) Sometimes the result is smoothed to get a continuous `rate' variable. The spike density of the PSTH is usually reported in units of Hz and often called the (time-dependent) firing rate of the neuron. 10: Definition of the spike density in the Peri-Stimulus-Time Histogram (PSTH) as an average over several runs of the experiment. As an experimental procedure, the spike density measure is a useful method to evaluate neuronal activity, in particular in the case of time-dependent stimuli. The obvious problem with this approach is that it can not be the decoding scheme used by neurons in the brain.
The Hodgkin-Huxley model can be understood with the help of Fig. 2. The semipermeable cell membrane separates the interior of the cell from the extracellular liquid and acts as a capacitor. If an input current I(t) is injected into the cell, it may add further charge on the capacitor, or leak through the channels in the cell membrane. Because of active ion transport through the cell membrane, the ion concentration inside the cell is different from that in the extracellular liquid. The Nernst potential generated by the difference in ion concentration is represented by a battery.