Solving system of nonlinear differential equation in MAPLE
$begingroup$
I'am working out on nonlinear differential equation and I need to find the equilibrium point which means all the system is equal to zero.
Here is the System of Diferential Equation:
begin{align*}
frac{dS}{dt} &= alpha - beta SV - delta S \
frac{dI}{dt} &= beta SV - sigma I \
frac{dV}{dt} &= mu nI - gamma_1 V - gamma_2 V - gamma_3 V - beta SV
end{align*}
then, to find the equilibrium point set $frac{dS}{dt} = frac{dI}{dI} = frac{dV}{dt} = 0$. It means that I have to solve the system of equation
begin{align*}
alpha - beta SV - delta S &=0 \
beta SV - sigma I &= 0\
mu nI - gamma_1 V - gamma_2 V - gamma_3 V - beta SV &=0
end{align*}
I've got the result by solving it manually but Can I use MAPLE software to solve this problem?
What I've done manually:
$V = frac{alpha - delta S}{beta S}, I = frac{alpha - delta S}{sigma}, S = frac{alpha}{delta} text{ or } S = frac{(gamma_1 +gamma_2+gamma_3)sigma}{beta(mu n - sigma)} $
maple
asked Dec 22 '18 at 11:42
SutMarSutMar
1007
$endgroup$
add a comment |
$begingroup$
I'am working out on nonlinear differential equation and I need to find the equilibrium point which means all the system is equal to zero.
Here is the System of Diferential Equation:
begin{align*}
frac{dS}{dt} &= alpha - beta SV - delta S \
frac{dI}{dt} &= beta SV - sigma I \
frac{dV}{dt} &= mu nI - gamma_1 V - gamma_2 V - gamma_3 V - beta SV
end{align*}
then, to find the equilibrium point set $frac{dS}{dt} = frac{dI}{dI} = frac{dV}{dt} = 0$. It means that I have to solve the system of equation
begin{align*}
alpha - beta SV - delta S &=0 \
beta SV - sigma I &= 0\
mu nI - gamma_1 V - gamma_2 V - gamma_3 V - beta SV &=0
end{align*}
I've got the result by solving it manually but Can I use MAPLE software to solve this problem?
What I've done manually:
$V = frac{alpha - delta S}{beta S}, I = frac{alpha - delta S}{sigma}, S = frac{alpha}{delta} text{ or } S = frac{(gamma_1 +gamma_2+gamma_3)sigma}{beta(mu n - sigma)} $
maple
asked Dec 22 '18 at 11:42
SutMarSutMar
1007
$endgroup$
$begingroup$
What result have you got?
$endgroup$
– Dr. Sonnhard Graubner
Dec 22 '18 at 11:50
$begingroup$
I've made some changes to my post @Dr.SonnhardGraubner
$endgroup$
– SutMar
Dec 22 '18 at 12:06
$begingroup$
I have solved it with Maple and now?
$endgroup$
– Dr. Sonnhard Graubner
Dec 22 '18 at 12:29
$begingroup$
I will feel happy if you are willing to teach it to me.
$endgroup$
– SutMar
Dec 22 '18 at 13:04
add a comment |
$begingroup$
I'am working out on nonlinear differential equation and I need to find the equilibrium point which means all the system is equal to zero.
Here is the System of Diferential Equation:
begin{align*}
frac{dS}{dt} &= alpha - beta SV - delta S \
frac{dI}{dt} &= beta SV - sigma I \
frac{dV}{dt} &= mu nI - gamma_1 V - gamma_2 V - gamma_3 V - beta SV
end{align*}
then, to find the equilibrium point set $frac{dS}{dt} = frac{dI}{dI} = frac{dV}{dt} = 0$. It means that I have to solve the system of equation
begin{align*}
alpha - beta SV - delta S &=0 \
beta SV - sigma I &= 0\
mu nI - gamma_1 V - gamma_2 V - gamma_3 V - beta SV &=0
end{align*}
I've got the result by solving it manually but Can I use MAPLE software to solve this problem?
What I've done manually:
$V = frac{alpha - delta S}{beta S}, I = frac{alpha - delta S}{sigma}, S = frac{alpha}{delta} text{ or } S = frac{(gamma_1 +gamma_2+gamma_3)sigma}{beta(mu n - sigma)} $
maple
asked Dec 22 '18 at 11:42
SutMarSutMar
1007
$endgroup$
I'am working out on nonlinear differential equation and I need to find the equilibrium point which means all the system is equal to zero.
Here is the System of Diferential Equation:
begin{align*}
frac{dS}{dt} &= alpha - beta SV - delta S \
frac{dI}{dt} &= beta SV - sigma I \
frac{dV}{dt} &= mu nI - gamma_1 V - gamma_2 V - gamma_3 V - beta SV
end{align*}
then, to find the equilibrium point set $frac{dS}{dt} = frac{dI}{dI} = frac{dV}{dt} = 0$. It means that I have to solve the system of equation
begin{align*}
alpha - beta SV - delta S &=0 \
beta SV - sigma I &= 0\
mu nI - gamma_1 V - gamma_2 V - gamma_3 V - beta SV &=0
end{align*}
I've got the result by solving it manually but Can I use MAPLE software to solve this problem?
What I've done manually:
$V = frac{alpha - delta S}{beta S}, I = frac{alpha - delta S}{sigma}, S = frac{alpha}{delta} text{ or } S = frac{(gamma_1 +gamma_2+gamma_3)sigma}{beta(mu n - sigma)} $
maple
maple
asked Dec 22 '18 at 11:42
SutMarSutMar
1007
asked Dec 22 '18 at 11:42
SutMarSutMar
1007
edited Dec 22 '18 at 12:05
SutMar
asked Dec 22 '18 at 11:42
SutMarSutMar
1007
asked Dec 22 '18 at 11:42
SutMarSutMar
1007
asked Dec 22 '18 at 11:42
SutMarSutMar
1007
1007
$begingroup$
What result have you got?
$endgroup$
– Dr. Sonnhard Graubner
Dec 22 '18 at 11:50
$begingroup$
I've made some changes to my post @Dr.SonnhardGraubner
$endgroup$
– SutMar
Dec 22 '18 at 12:06
$begingroup$
I have solved it with Maple and now?
$endgroup$
– Dr. Sonnhard Graubner
Dec 22 '18 at 12:29
$begingroup$
I will feel happy if you are willing to teach it to me.
$endgroup$
– SutMar
Dec 22 '18 at 13:04
add a comment |
$begingroup$
What result have you got?
$endgroup$
– Dr. Sonnhard Graubner
Dec 22 '18 at 11:50
$begingroup$
I've made some changes to my post @Dr.SonnhardGraubner
$endgroup$
– SutMar
Dec 22 '18 at 12:06
$begingroup$
I have solved it with Maple and now?
$endgroup$
– Dr. Sonnhard Graubner
Dec 22 '18 at 12:29
$begingroup$
I will feel happy if you are willing to teach it to me.
$endgroup$
– SutMar
Dec 22 '18 at 13:04
$begingroup$
What result have you got?
$endgroup$
– Dr. Sonnhard Graubner
Dec 22 '18 at 11:50
$begingroup$
What result have you got?
$endgroup$
– Dr. Sonnhard Graubner
Dec 22 '18 at 11:50
$begingroup$
I've made some changes to my post @Dr.SonnhardGraubner
$endgroup$
– SutMar
Dec 22 '18 at 12:06
$begingroup$
I've made some changes to my post @Dr.SonnhardGraubner
$endgroup$
– SutMar
Dec 22 '18 at 12:06
$begingroup$
I have solved it with Maple and now?
$endgroup$
– Dr. Sonnhard Graubner
Dec 22 '18 at 12:29
$begingroup$
I have solved it with Maple and now?
$endgroup$
– Dr. Sonnhard Graubner
Dec 22 '18 at 12:29
$begingroup$
I will feel happy if you are willing to teach it to me.
$endgroup$
– SutMar
Dec 22 '18 at 13:04
$begingroup$
I will feel happy if you are willing to teach it to me.
$endgroup$
– SutMar
Dec 22 '18 at 13:04
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Here is how to do it in Maple
eqs:={alpha-beta*S*V-delta*S,beta*S*V-sigma*II,mu*n*II-gamma[1]*V-gamma[2]*V-gamma[3]*V-beta*S*V};vars:={S,II,V};solve(eqs,vars);
Note that I is a reserved symbol in Maple, so I just used another symbol II for it.
Maple yields two solutions
$$
left{ {it II}=0,S={frac {alpha}{delta}},V=0 right}
$$
and
$$
left{ {it II}={frac {alpha,beta,mu,n-alpha,beta,sigma-
delta,sigma,gamma_{{1}}-delta,sigma,gamma_{{2}}-delta,
sigma,gamma_{{3}}}{beta,sigma, left( mu,n-sigma right) }},
S={frac {sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}}
right) }{beta, left( mu,n-sigma right) }},
\
V={frac {alpha,
beta,mu,n-alpha,beta,sigma-delta,sigma,gamma_{{1}}-
delta,sigma,gamma_{{2}}-delta,sigma,gamma_{{3}}}{beta,
sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}} right) }}
right}
$$
answered Dec 22 '18 at 13:08
GEdgarGEdgar
62.7k267171
$endgroup$
add a comment |
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1 Answer
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active
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votes
1 Answer
1
active
oldest
votes
active
oldest
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oldest
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$begingroup$
Here is how to do it in Maple
eqs:={alpha-beta*S*V-delta*S,beta*S*V-sigma*II,mu*n*II-gamma[1]*V-gamma[2]*V-gamma[3]*V-beta*S*V};vars:={S,II,V};solve(eqs,vars);
Note that I is a reserved symbol in Maple, so I just used another symbol II for it.
Maple yields two solutions
$$
left{ {it II}=0,S={frac {alpha}{delta}},V=0 right}
$$
and
$$
left{ {it II}={frac {alpha,beta,mu,n-alpha,beta,sigma-
delta,sigma,gamma_{{1}}-delta,sigma,gamma_{{2}}-delta,
sigma,gamma_{{3}}}{beta,sigma, left( mu,n-sigma right) }},
S={frac {sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}}
right) }{beta, left( mu,n-sigma right) }},
\
V={frac {alpha,
beta,mu,n-alpha,beta,sigma-delta,sigma,gamma_{{1}}-
delta,sigma,gamma_{{2}}-delta,sigma,gamma_{{3}}}{beta,
sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}} right) }}
right}
$$
answered Dec 22 '18 at 13:08
GEdgarGEdgar
62.7k267171
$endgroup$
add a comment |
$begingroup$
Here is how to do it in Maple
eqs:={alpha-beta*S*V-delta*S,beta*S*V-sigma*II,mu*n*II-gamma[1]*V-gamma[2]*V-gamma[3]*V-beta*S*V};vars:={S,II,V};solve(eqs,vars);
Note that I is a reserved symbol in Maple, so I just used another symbol II for it.
Maple yields two solutions
$$
left{ {it II}=0,S={frac {alpha}{delta}},V=0 right}
$$
and
$$
left{ {it II}={frac {alpha,beta,mu,n-alpha,beta,sigma-
delta,sigma,gamma_{{1}}-delta,sigma,gamma_{{2}}-delta,
sigma,gamma_{{3}}}{beta,sigma, left( mu,n-sigma right) }},
S={frac {sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}}
right) }{beta, left( mu,n-sigma right) }},
\
V={frac {alpha,
beta,mu,n-alpha,beta,sigma-delta,sigma,gamma_{{1}}-
delta,sigma,gamma_{{2}}-delta,sigma,gamma_{{3}}}{beta,
sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}} right) }}
right}
$$
answered Dec 22 '18 at 13:08
GEdgarGEdgar
62.7k267171
$endgroup$
add a comment |
$begingroup$
Here is how to do it in Maple
eqs:={alpha-beta*S*V-delta*S,beta*S*V-sigma*II,mu*n*II-gamma[1]*V-gamma[2]*V-gamma[3]*V-beta*S*V};vars:={S,II,V};solve(eqs,vars);
Note that I is a reserved symbol in Maple, so I just used another symbol II for it.
Maple yields two solutions
$$
left{ {it II}=0,S={frac {alpha}{delta}},V=0 right}
$$
and
$$
left{ {it II}={frac {alpha,beta,mu,n-alpha,beta,sigma-
delta,sigma,gamma_{{1}}-delta,sigma,gamma_{{2}}-delta,
sigma,gamma_{{3}}}{beta,sigma, left( mu,n-sigma right) }},
S={frac {sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}}
right) }{beta, left( mu,n-sigma right) }},
\
V={frac {alpha,
beta,mu,n-alpha,beta,sigma-delta,sigma,gamma_{{1}}-
delta,sigma,gamma_{{2}}-delta,sigma,gamma_{{3}}}{beta,
sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}} right) }}
right}
$$
answered Dec 22 '18 at 13:08
GEdgarGEdgar
62.7k267171
$endgroup$
Here is how to do it in Maple
eqs:={alpha-beta*S*V-delta*S,beta*S*V-sigma*II,mu*n*II-gamma[1]*V-gamma[2]*V-gamma[3]*V-beta*S*V};vars:={S,II,V};solve(eqs,vars);
Note that I is a reserved symbol in Maple, so I just used another symbol II for it.
Maple yields two solutions
$$
left{ {it II}=0,S={frac {alpha}{delta}},V=0 right}
$$
and
$$
left{ {it II}={frac {alpha,beta,mu,n-alpha,beta,sigma-
delta,sigma,gamma_{{1}}-delta,sigma,gamma_{{2}}-delta,
sigma,gamma_{{3}}}{beta,sigma, left( mu,n-sigma right) }},
S={frac {sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}}
right) }{beta, left( mu,n-sigma right) }},
\
V={frac {alpha,
beta,mu,n-alpha,beta,sigma-delta,sigma,gamma_{{1}}-
delta,sigma,gamma_{{2}}-delta,sigma,gamma_{{3}}}{beta,
sigma, left( gamma_{{1}}+gamma_{{2}}+gamma_{{3}} right) }}
right}
$$
answered Dec 22 '18 at 13:08
GEdgarGEdgar
62.7k267171
answered Dec 22 '18 at 13:08
GEdgarGEdgar
62.7k267171
answered Dec 22 '18 at 13:08
GEdgarGEdgar
62.7k267171
answered Dec 22 '18 at 13:08
GEdgarGEdgar
62.7k267171
62.7k267171
add a comment |
add a comment |
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$begingroup$
What result have you got?
$endgroup$
– Dr. Sonnhard Graubner
Dec 22 '18 at 11:50
$begingroup$
I've made some changes to my post @Dr.SonnhardGraubner
$endgroup$
– SutMar
Dec 22 '18 at 12:06
$begingroup$
I have solved it with Maple and now?
$endgroup$
– Dr. Sonnhard Graubner
Dec 22 '18 at 12:29
$begingroup$
I will feel happy if you are willing to teach it to me.
$endgroup$
– SutMar
Dec 22 '18 at 13:04