# Command: growth_curve_linear

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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:

- SynapticElement
- SPManager
- SPBuilder
- GrowthCurveLinear
- GrowthCurveGaussian

Source:

    /opt/conda/conda-bld/nest_1512418852064/work/nest-2.12.0/nestkernel/growth_curve.h

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