**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:**

**Source:**

/home/nest/work/nest-2.14.0/nestkernel/growth_curve.h