How to derive the time dependent Leaky Integrator and Fire?
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The general time-dependent LIF model solution is:
$$
u(t) = u_textrest exp left(-fract-t_0tau_mright) + fracRtau_mint_0^t-t_0 expleft(-fracstau_mright) , I(t-s) ,mathrm d s
$$
From the LIF equation
$$
tau_m fracdudt = R I(t) - [u(t) - u_textrest]
$$
According to this paper, equation 7.
It is assumed $t_0$ is the beginning of the time interval, at which $u(t)$ is at it's minimum and that $I(t)$ can vary. I have no idea where to even start, thank you.
differential-equations mathematical-modeling neural-networks
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up vote
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down vote
favorite
The general time-dependent LIF model solution is:
$$
u(t) = u_textrest exp left(-fract-t_0tau_mright) + fracRtau_mint_0^t-t_0 expleft(-fracstau_mright) , I(t-s) ,mathrm d s
$$
From the LIF equation
$$
tau_m fracdudt = R I(t) - [u(t) - u_textrest]
$$
According to this paper, equation 7.
It is assumed $t_0$ is the beginning of the time interval, at which $u(t)$ is at it's minimum and that $I(t)$ can vary. I have no idea where to even start, thank you.
differential-equations mathematical-modeling neural-networks
Could you please clarify what exactly are you asking? Do you want to understand how to solve LIF equation?
â Evgeny
Aug 20 at 9:52
Yes, or a step by step derivation of the general LIF so that I can understand it.
â John Miller
Aug 20 at 12:01
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
The general time-dependent LIF model solution is:
$$
u(t) = u_textrest exp left(-fract-t_0tau_mright) + fracRtau_mint_0^t-t_0 expleft(-fracstau_mright) , I(t-s) ,mathrm d s
$$
From the LIF equation
$$
tau_m fracdudt = R I(t) - [u(t) - u_textrest]
$$
According to this paper, equation 7.
It is assumed $t_0$ is the beginning of the time interval, at which $u(t)$ is at it's minimum and that $I(t)$ can vary. I have no idea where to even start, thank you.
differential-equations mathematical-modeling neural-networks
The general time-dependent LIF model solution is:
$$
u(t) = u_textrest exp left(-fract-t_0tau_mright) + fracRtau_mint_0^t-t_0 expleft(-fracstau_mright) , I(t-s) ,mathrm d s
$$
From the LIF equation
$$
tau_m fracdudt = R I(t) - [u(t) - u_textrest]
$$
According to this paper, equation 7.
It is assumed $t_0$ is the beginning of the time interval, at which $u(t)$ is at it's minimum and that $I(t)$ can vary. I have no idea where to even start, thank you.
differential-equations mathematical-modeling neural-networks
edited Aug 19 at 10:49
Rodrigo de Azevedo
12.6k41751
12.6k41751
asked Aug 19 at 10:45
John Miller
946
946
Could you please clarify what exactly are you asking? Do you want to understand how to solve LIF equation?
â Evgeny
Aug 20 at 9:52
Yes, or a step by step derivation of the general LIF so that I can understand it.
â John Miller
Aug 20 at 12:01
add a comment |Â
Could you please clarify what exactly are you asking? Do you want to understand how to solve LIF equation?
â Evgeny
Aug 20 at 9:52
Yes, or a step by step derivation of the general LIF so that I can understand it.
â John Miller
Aug 20 at 12:01
Could you please clarify what exactly are you asking? Do you want to understand how to solve LIF equation?
â Evgeny
Aug 20 at 9:52
Could you please clarify what exactly are you asking? Do you want to understand how to solve LIF equation?
â Evgeny
Aug 20 at 9:52
Yes, or a step by step derivation of the general LIF so that I can understand it.
â John Miller
Aug 20 at 12:01
Yes, or a step by step derivation of the general LIF so that I can understand it.
â John Miller
Aug 20 at 12:01
add a comment |Â
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Could you please clarify what exactly are you asking? Do you want to understand how to solve LIF equation?
â Evgeny
Aug 20 at 9:52
Yes, or a step by step derivation of the general LIF so that I can understand it.
â John Miller
Aug 20 at 12:01