Neironu uzvedības modelēšana ar diferenču vienādojumiem
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Latvijas Universitāte
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Abstract
Maģistra darbā aplūkots diferenču vienādojums
f(x(n+1))=b*f(x(n))-f(x(n-k)), n=0,1,2...
kā modelis vienam neironam, kur funkcija f : R->R ir gabaliem lineāra signālfunkcija. Ja b=1, tad visi vienādojuma atrisinājumi ir lauzti periodiski – šis gadījums ir aprakstīts literatūrā [2]. Darba novitāte ir gadījuma 0<b<1 izpēte. Pierādīti rezultāti, kādās situācijās diferenču vienādojuma atrisinājumi konverģē uz stacionārajiem punktiem 1/(1-b) un -1/(1-b).
Darbs ilustrēts ar piemēriem, kuri iegūti ar MS Excel un Maple palīdzību.
In the present master paper the difference equation f(x(n+1))=b*f(x(n))-f(x(n-k)), n=0,1,2,... is discussed as a model for a single neuron, where function f : R->R is piecewise – linear signal function. If b=1 then every solution is truncated periodic – this situation is shown in literature [2]. The novelty of the paper is research of difference equation f(x(n+1))=b*f(x(n))-f(x(n-k)) when b<0<1. It has been proved in what situations solutions converge to the stationary points 1/(1-b)and -1/(1-b). The research paper is illustrated with examples which have been made with the help of MS Excel and Maple.
In the present master paper the difference equation f(x(n+1))=b*f(x(n))-f(x(n-k)), n=0,1,2,... is discussed as a model for a single neuron, where function f : R->R is piecewise – linear signal function. If b=1 then every solution is truncated periodic – this situation is shown in literature [2]. The novelty of the paper is research of difference equation f(x(n+1))=b*f(x(n))-f(x(n-k)) when b<0<1. It has been proved in what situations solutions converge to the stationary points 1/(1-b)and -1/(1-b). The research paper is illustrated with examples which have been made with the help of MS Excel and Maple.