growth_curve_linear - Linear version of a growth curve
This class represents a linear growth rule for the number of synaptic
elements inside a neuron. The creation and deletion of synaptic elements
when structural plasticity is enabled, allows the dynamic rewiring of the
network during the simulation.
This type of growth curve uses an exact integration method to update the
number of synaptic elements: dz/dt = nu (1 - (1/eps) * Ca(t)), where nu is
the growth rate [elements/ms] and eps is the desired average calcium
concentration. The growth rate nu is defined in the SynapticElement class.

eps double - The target calcium concentration that
the neuron should look to achieve by creating or
deleting synaptic elements. It should always be a
positive value. It is important to note that the
calcium concentration is linearly proportional to the
firing rate. This is because dCa/dt = - Ca(t)/tau_Ca
+ beta_Ca if the neuron fires and dCa/dt = -
Ca(t)/tau_Ca otherwise, where tau_Ca is the calcium
concentration decay constant and beta_Ca is the
calcium intake constant (see SynapticElement class).
This means that eps also defines the desired firing
rate that the neuron should achieve. For example, an
eps = 0.05 [Ca2+] with tau_Ca = 10000.0 and beta_Ca =
0.001 for a synaptic element means a desired firing
rate of 5Hz.

[1] Butz, Markus, Florentin Wörgötter, and Arjen van Ooyen.
"Activity-dependent structural plasticity." Brain research reviews 60.2
(2009): 287-305.

[2] Butz, Markus, and Arjen van Ooyen. "A simple rule for dendritic spine
and axonal bouton formation can account for cortical reorganization after
focal retinal lesions." PLoS Comput Biol 9.10 (2013): e1003259.

Mikael Naveau  
July 2013  
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