Computational Modeling Methods for Neuroscientists by Erik De Schutter

By Erik De Schutter

A advisor to computational modeling tools in neuroscience, overlaying a diversity of modeling scales from molecular reactions to giant neural networks.

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Our main goal here has been to demonstrate the benefits and insights obtained from a geometric approach and how you can predict qualitative behavior if you develop a little intuition about how the nullclines depend on system parameters. For example, you could easily imagine that changing some parameters could distort the nullclines and lead to multiple intersections (therefore, multiple steady states) and possibilities for multistability and SNIC bifurcations. , by looking at projections that show a fast and a slow variable.

4a shows the potentials in three di¤erent compartments, 50, 60, and 70. The time di¤erence between the action potential at j ¼ 50 and j ¼ 60 is exactly the same as that between j ¼ 60 and j ¼ 70. This is the hallmark of a traveling wave. 4b shows the full space-time picture. Time increases from left to right and compartment number increases from top to bottom. The potential is shown as a 20 Bard Ermentrout and John Rinzel grayscale and traces out a straight line except near the ends of the cable.

Some extra ‘‘genetic drift’’ is generated by the mutation operator, which transforms individuals in a stochastic way. When the breeding and mutating processes are complete, the survivor selection operator is used to select which individuals will form the next generation. The name ‘‘evolutionary computing’’ is a broad term and has subdomains. Three of these are genetic algorithms (GA), evolutionary strategies (ES), and di¤erential evolutions (DE). Genetic algorithms were developed in the 1960s and made widely known by Holland in the 1970s (Holland, 1975).

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