How to model this simple logic circuit using dynamical systems techniques.
$begingroup$
I would like to mathematically model this simple logic circuit:
In addition, the input to input1 of this gate would also be some function that looked something like this:
Given a continuous function $f(x1,x2)$ that represents OR1, and a continuous function $g(x)$ that represents input into input1, how could dynamical system techniques be used to model this as a continuous non-linear system? Having no training in dynamical systems I'm not sure where to start. What would be a good textbook or tutorial that could help me start making progress with this?
ordinary-differential-equations dynamical-systems
asked Jan 2 at 20:58
C ShreveC Shreve
27016
$endgroup$
|
show 2 more comments
$begingroup$
I would like to mathematically model this simple logic circuit:
In addition, the input to input1 of this gate would also be some function that looked something like this:
Given a continuous function $f(x1,x2)$ that represents OR1, and a continuous function $g(x)$ that represents input into input1, how could dynamical system techniques be used to model this as a continuous non-linear system? Having no training in dynamical systems I'm not sure where to start. What would be a good textbook or tutorial that could help me start making progress with this?
ordinary-differential-equations dynamical-systems
asked Jan 2 at 20:58
C ShreveC Shreve
27016
$endgroup$
$begingroup$
Are you using the "or" gate symbol to represent a continuous function or are you assuming there is a continuous function that represents the "or" gate?
$endgroup$
– John Douma
Jan 2 at 21:15
$begingroup$
Is the loop to be interpreted asin2[k]=out[k-1], that isout[k] = in1[k] or out[k-1]? And you are looking for a continuous version of this?
$endgroup$
– LutzL
Jan 2 at 21:41
$begingroup$
@JohnDouma - this is assuming $f(x1,x2)$ is a continuous function that represents the 'or' gate.
$endgroup$
– C Shreve
Jan 3 at 1:02
$begingroup$
@Lutlz - loop is to be interpreted as $out[k] = in1[k] or out[k-1]$ and yes...looking for a continuous version. Please assume $f(x1,x2)$ is a continuous function that represents the OR function.
$endgroup$
– C Shreve
Jan 3 at 1:04
$begingroup$
There is no continuous function that models an or gate. Think about bootstrapping the system. The output will be $0$ and as soon as $ggt 0$, the gate will abruptly switch to $1$.
$endgroup$
– John Douma
Jan 3 at 1:37
|
show 2 more comments
$begingroup$
I would like to mathematically model this simple logic circuit:
In addition, the input to input1 of this gate would also be some function that looked something like this:
Given a continuous function $f(x1,x2)$ that represents OR1, and a continuous function $g(x)$ that represents input into input1, how could dynamical system techniques be used to model this as a continuous non-linear system? Having no training in dynamical systems I'm not sure where to start. What would be a good textbook or tutorial that could help me start making progress with this?
ordinary-differential-equations dynamical-systems
asked Jan 2 at 20:58
C ShreveC Shreve
27016
$endgroup$
I would like to mathematically model this simple logic circuit:
In addition, the input to input1 of this gate would also be some function that looked something like this:
Given a continuous function $f(x1,x2)$ that represents OR1, and a continuous function $g(x)$ that represents input into input1, how could dynamical system techniques be used to model this as a continuous non-linear system? Having no training in dynamical systems I'm not sure where to start. What would be a good textbook or tutorial that could help me start making progress with this?
ordinary-differential-equations dynamical-systems
ordinary-differential-equations dynamical-systems
asked Jan 2 at 20:58
C ShreveC Shreve
27016
asked Jan 2 at 20:58
C ShreveC Shreve
27016
asked Jan 2 at 20:58
C ShreveC Shreve
27016
asked Jan 2 at 20:58
C ShreveC Shreve
27016
asked Jan 2 at 20:58
C ShreveC Shreve
27016
27016
$begingroup$
Are you using the "or" gate symbol to represent a continuous function or are you assuming there is a continuous function that represents the "or" gate?
$endgroup$
– John Douma
Jan 2 at 21:15
$begingroup$
Is the loop to be interpreted asin2[k]=out[k-1], that isout[k] = in1[k] or out[k-1]? And you are looking for a continuous version of this?
$endgroup$
– LutzL
Jan 2 at 21:41
$begingroup$
@JohnDouma - this is assuming $f(x1,x2)$ is a continuous function that represents the 'or' gate.
$endgroup$
– C Shreve
Jan 3 at 1:02
$begingroup$
@Lutlz - loop is to be interpreted as $out[k] = in1[k] or out[k-1]$ and yes...looking for a continuous version. Please assume $f(x1,x2)$ is a continuous function that represents the OR function.
$endgroup$
– C Shreve
Jan 3 at 1:04
$begingroup$
There is no continuous function that models an or gate. Think about bootstrapping the system. The output will be $0$ and as soon as $ggt 0$, the gate will abruptly switch to $1$.
$endgroup$
– John Douma
Jan 3 at 1:37
|
show 2 more comments
$begingroup$
Are you using the "or" gate symbol to represent a continuous function or are you assuming there is a continuous function that represents the "or" gate?
$endgroup$
– John Douma
Jan 2 at 21:15
$begingroup$
Is the loop to be interpreted asin2[k]=out[k-1], that isout[k] = in1[k] or out[k-1]? And you are looking for a continuous version of this?
$endgroup$
– LutzL
Jan 2 at 21:41
$begingroup$
@JohnDouma - this is assuming $f(x1,x2)$ is a continuous function that represents the 'or' gate.
$endgroup$
– C Shreve
Jan 3 at 1:02
$begingroup$
@Lutlz - loop is to be interpreted as $out[k] = in1[k] or out[k-1]$ and yes...looking for a continuous version. Please assume $f(x1,x2)$ is a continuous function that represents the OR function.
$endgroup$
– C Shreve
Jan 3 at 1:04
$begingroup$
There is no continuous function that models an or gate. Think about bootstrapping the system. The output will be $0$ and as soon as $ggt 0$, the gate will abruptly switch to $1$.
$endgroup$
– John Douma
Jan 3 at 1:37
$begingroup$
Are you using the "or" gate symbol to represent a continuous function or are you assuming there is a continuous function that represents the "or" gate?
$endgroup$
– John Douma
Jan 2 at 21:15
$begingroup$
Are you using the "or" gate symbol to represent a continuous function or are you assuming there is a continuous function that represents the "or" gate?
$endgroup$
– John Douma
Jan 2 at 21:15
$begingroup$
Is the loop to be interpreted as
in2[k]=out[k-1], that is out[k] = in1[k] or out[k-1]? And you are looking for a continuous version of this?$endgroup$
– LutzL
Jan 2 at 21:41
$begingroup$
Is the loop to be interpreted as
in2[k]=out[k-1], that is out[k] = in1[k] or out[k-1]? And you are looking for a continuous version of this?$endgroup$
– LutzL
Jan 2 at 21:41
$begingroup$
@JohnDouma - this is assuming $f(x1,x2)$ is a continuous function that represents the 'or' gate.
$endgroup$
– C Shreve
Jan 3 at 1:02
$begingroup$
@JohnDouma - this is assuming $f(x1,x2)$ is a continuous function that represents the 'or' gate.
$endgroup$
– C Shreve
Jan 3 at 1:02
$begingroup$
@Lutlz - loop is to be interpreted as $out[k] = in1[k] or out[k-1]$ and yes...looking for a continuous version. Please assume $f(x1,x2)$ is a continuous function that represents the OR function.
$endgroup$
– C Shreve
Jan 3 at 1:04
$begingroup$
@Lutlz - loop is to be interpreted as $out[k] = in1[k] or out[k-1]$ and yes...looking for a continuous version. Please assume $f(x1,x2)$ is a continuous function that represents the OR function.
$endgroup$
– C Shreve
Jan 3 at 1:04
$begingroup$
There is no continuous function that models an or gate. Think about bootstrapping the system. The output will be $0$ and as soon as $ggt 0$, the gate will abruptly switch to $1$.
$endgroup$
– John Douma
Jan 3 at 1:37
$begingroup$
There is no continuous function that models an or gate. Think about bootstrapping the system. The output will be $0$ and as soon as $ggt 0$, the gate will abruptly switch to $1$.
$endgroup$
– John Douma
Jan 3 at 1:37
|
show 2 more comments
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$begingroup$
Are you using the "or" gate symbol to represent a continuous function or are you assuming there is a continuous function that represents the "or" gate?
$endgroup$
– John Douma
Jan 2 at 21:15
$begingroup$
Is the loop to be interpreted as
in2[k]=out[k-1], that isout[k] = in1[k] or out[k-1]? And you are looking for a continuous version of this?$endgroup$
– LutzL
Jan 2 at 21:41
$begingroup$
@JohnDouma - this is assuming $f(x1,x2)$ is a continuous function that represents the 'or' gate.
$endgroup$
– C Shreve
Jan 3 at 1:02
$begingroup$
@Lutlz - loop is to be interpreted as $out[k] = in1[k] or out[k-1]$ and yes...looking for a continuous version. Please assume $f(x1,x2)$ is a continuous function that represents the OR function.
$endgroup$
– C Shreve
Jan 3 at 1:04
$begingroup$
There is no continuous function that models an or gate. Think about bootstrapping the system. The output will be $0$ and as soon as $ggt 0$, the gate will abruptly switch to $1$.
$endgroup$
– John Douma
Jan 3 at 1:37