Leech Heart Interneuron model (Sharma et al 2020)

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Fractional order Leech heart interneuron model is investigated. Different firing properties are explored. In this article, we investigate the alternation of spiking and bursting phenomena of an uncoupled and coupled fractional Leech-Heart (L-H) neurons. We show that a complete graph of heterogeneous de-synchronized neurons in the backdrop of diverse memory settings (a mixture of integer and fractional exponents) can eventually lead to bursting with the formation of cluster synchronization over a certain threshold of coupling strength, however, the uncoupled L-H neurons cannot reveal bursting dynamics. Using the stability analysis in fractional domain, we demarcate the parameter space where the quiescent or steady-state emerges in uncoupled L-H neuron. Finally, a reduced-order model is introduced to capture the activities of the large network of fractional-order model neurons.
1 . Sharma SK, Mondal A, Mondal A, Upadhyay RK, Hens C (2020) Emergence of bursting in a network of memory dependent excitable and spiking leech-heart neurons. J R Soc Interface 17:20190859 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism: Leech;
Cell Type(s): Leech heart interneuron;
Gap Junctions:
Simulation Environment: MATLAB;
Model Concept(s): Oscillations; Bifurcation;
function [maxtab, mintab]=peakdet(v, delta, x)
%PEAKDET Detect peaks in a vector
%        [MAXTAB, MINTAB] = PEAKDET(V, DELTA) finds the local
%        maxima and minima ("peaks") in the vector V.
%        MAXTAB and MINTAB consists of two columns. Column 1
%        contains indices in V, and column 2 the found values.
%        With [MAXTAB, MINTAB] = PEAKDET(V, DELTA, X) the indices
%        in MAXTAB and MINTAB are replaced with the corresponding
%        X-values.
%        A point is considered a maximum peak if it has the maximal
%        value, and was preceded (to the left) by a value lower by
%        DELTA.

% Eli Billauer, 3.4.05 (Explicitly not copyrighted).
% This function is released to the public domain; Any use is allowed.

maxtab = [];
mintab = [];

v = v(:); % Just in case this wasn't a proper vector

if nargin< 3
  x = (1:length(v))';
  x = x(:);
if length(v)~= length(x)
error('Input vectors v and x must have same length');

if (length(delta(:)))>1
error('Input argument DELTA must be a scalar');

if delta <= 0
error('Input argument DELTA must be positive');

mn = Inf; mx = -Inf;
mnpos = NaN; mxpos = NaN;

lookformax = 1;

for i=1:length(v)
this = v(i);
if this > mx, mx = this; mxpos = x(i); end
if this <mn, mn = this; mnpos = x(i); end

if lookformax
if this < mx-delta
maxtab = [maxtab ; mxpos mx];
mn = this; mnpos = x(i);
lookformax = 0;
if this >mn+delta
mintab = [mintab ; mnpos mn];
mx = this; mxpos = x(i);
lookformax = 1;

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