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Delay differential equations

Erik A. Roberts edited this page May 16, 2018 · 10 revisions

Delay differential equations (e.g., axonal delays in network of HH neurons)

This example demonstrates:

  1. creating delay differential equations with X(t-delay)
  2. defining mechanisms (e.g., iampa) in the same script as the full model specification and storing them using the specification.mechanisms field.
ampa_with_delay={
  'gSYN=.1; ESYN=0; tauD=2; tauR=0.4; delay=20'
  'netcon=ones(N_pre,N_post)'                                         % connectivity matrix
  'ISYN(V,s)=-gSYN.*(s*netcon).*(V-ESYN)'                             % synaptic current
  'ds/dt=-s./tauD+((1-s)/tauR).*(1+tanh(V_pre(t-delay)/10)); s(0)=.1' % gate with 20ms delay
  '@current += ISYN(V_post,s)'
};

s=[];
s.populations(1).name='HH';
s.populations(1).equations='dV/dt=@current+10*(t<50);{iNa,iK};V(0)=-65';
s.connections(1).direction='HH->HH';
s.connections(1).mechanism_list='iampa';
s.connections(1).parameters={'gSYN',.1};
s.mechanisms(1).name='iampa';
s.mechanisms(1).equations=ampa_with_delay;
data=dsSimulate(s,'time_limits',[0 100]);
figure; plot(data.time,data.HH_V);

An example integrate-and-fire network with axonal delays can be found here.