Post by Alireza on Jun 8, 2016 14:43:15 GMT
Reading the following paper [1] I recalled few ideas I have been thinking in recent years. That is a balanced network works near a bifurcation point which is presumably a Hopf bifurcation. There are several cues for this arguments, first with a suitable set of parameters the system is in irregular-asynchronous state -- a fixed point in a mean-field perspective. Second in this regime system shows damped oscillations in response to external stimuli, say a synchronous pulse packet as you see in Fig.2 of the paper below. Third is with changing the parameters, the system begins to oscillate and produce rhythm, that is a limit cycle in mean-field view.
The third observation can be a result of another type of bifurcation, say SNIC but the second indicates it should be a Hopf one. For me the first question is why always Hopf bifurcation when we have no prior constraint on the constituent neurons? and when most of the simulations use LIF neurons which are sort of type-I.
The answer may be the feedback system of excitatory-inhibitory which is usually believed to be origin of the rhythms (although it is not always). It is interesting to inspect how presence of feedback changes the type of an excitable creature. Specific problems:
1- to study the bifurcation properties of an excitable system, say a model neuron of either type with a feedback (an autaptic connection). It can be interesting to show if both neuronal types result in Hopf bifurcation in presence of feedback! (see also [2])
2- If we accept the common sense that the inh-exc feedback loop is responsible for rhythmogenesis and it works simply like a two components loop, the feedback delay time is a decisive parameter. I haven't seen a modeling study with distributed delay times, have you? with constant delays it seems reasonable for feedback system to work but what happens in case of distributed delays?
[1] Hahn, Bujan, Fregnac, Aertsen, and Kumar, PLoS Comp Biol 10(8), e1003811 (2014)
[2] Hashemi, Valizadeh, and Azizi, PRE 85(2), 021917 (2012)
The third observation can be a result of another type of bifurcation, say SNIC but the second indicates it should be a Hopf one. For me the first question is why always Hopf bifurcation when we have no prior constraint on the constituent neurons? and when most of the simulations use LIF neurons which are sort of type-I.
The answer may be the feedback system of excitatory-inhibitory which is usually believed to be origin of the rhythms (although it is not always). It is interesting to inspect how presence of feedback changes the type of an excitable creature. Specific problems:
1- to study the bifurcation properties of an excitable system, say a model neuron of either type with a feedback (an autaptic connection). It can be interesting to show if both neuronal types result in Hopf bifurcation in presence of feedback! (see also [2])
2- If we accept the common sense that the inh-exc feedback loop is responsible for rhythmogenesis and it works simply like a two components loop, the feedback delay time is a decisive parameter. I haven't seen a modeling study with distributed delay times, have you? with constant delays it seems reasonable for feedback system to work but what happens in case of distributed delays?
[1] Hahn, Bujan, Fregnac, Aertsen, and Kumar, PLoS Comp Biol 10(8), e1003811 (2014)
[2] Hashemi, Valizadeh, and Azizi, PRE 85(2), 021917 (2012)