**Name:**

growth_curve_linear - Linear version of a growth curve

**Description:**

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.

**Parameters:**

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.

**References:**

[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.

**Author:**

Mikael Naveau

**FirstVersion:**

July 2013

**SeeAlso:**

**Source:**

/home/graber/work-nest/nest-git/nest-simulator/nestkernel/growth_curve.h