# Command: growth_curve_sigmoid

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Name:

    growth_curve_sigmoid - Sigmoid version of a growth curve

Description:

      This class represents a Sigmoid 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 / (1 + e^((Ca(t)	- eps)/psi)))	- 1)
      eps is the target mean calcium concentration in the
      neuron, psi controls the width of the sigmoid and nu is the growth rate in
      elements/ms. 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 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.

      psi	 double	-  Parameter that controls the width of the curve.
      Must be greater than 0

References:

      [1] Butz, Markus, Steenbuck, Ines D., and Arjen van Ooyen.
      "Homeostatic structural plasticity increases the efficiency of small-world
      networks." Frontiers in Synaptic Neuroscience 6 (2014): 7.

Author:

    Ankur Sinha

FirstVersion:

    September 2016

SeeAlso:

- SynapticElement
- SPManager
- SPBuilder
- GrowthCurveLinear
- GrowthCurveSigmoid

Source:

    /opt/conda/conda-bld/nest_1510213973486/work/nest-2.14.0/nestkernel/growth_curve.h

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