# Command: growth_curve_gaussian

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Name:

    growth_curve_gaussian - Gaussian version of a growth curve

Description:

      This class represents a Gaussian 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 a forward Euler integration method to update
      the number of synaptic elements:
      dz/dt = nu (2 * e^(- ((Ca(t)	- xi)/z)^2 )	- 1)
      where xi = (eta  + eps)/2,
      zeta = (eps	- eta)/2 * sqrt(ln(2))),
      eta is the minimum calcium concentration required for any synaptic element
      to be created, eps is the target mean calcium concentration in the neuron
      and nu is the growth rate in elements/ms. The growth rate nu is defined in
      the SynapticElement class.

Parameters:

      eta	 double	-  Minimum amount of calcium concentration that the
      neuron needs to start creating synaptic elements.
      eta can have a negative value, making the growth
      curve move its maximum to the left. For example, if
      eta=-0.5 and eps=0.5 [Ca2+], the maximum growth rate
      (elements/ms) will be achieved at 0.0 [Ca2+]. If
      eta=0.0 [Ca2+] and eps=0.5 [Ca2+] the maximum growth
      rate will be achieved at 0.25 [Ca2+] while at 0.0
      [Ca+2] no new elements will be created.

      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 can also be seen as 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.

      nu	 double	-  Growth rate in elements/ms. The growth rate nu is
      defined in the SynapticElement class. Can be negative.

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_1512421404550/work/nest-2.12.0/nestkernel/growth_curve.h

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