How to prove that there is no periodic orbit in this autonomous system?(ODE)
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Consider the autonomous system below with the parameters $aneq 0$ and $mn neq 0$:
$$begin{cases}
displaystylefrac{dx}{dt} &=-y+mxy+ny^2\
displaystylefrac{dy}{dt} &=x+ax^2
end{cases}$$
How to prove that there is no periodic orbit in this autonomous system?
I think maybe Dulac's criterion is the tips of this question, but I haven't found the Dulac's Function yet.
differential-equations dynamical-systems
edited Nov 17 at 13:31
Rebellos
12.5k21041
asked Nov 17 at 12:13
panyupj
111
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up vote
2
down vote
favorite
Consider the autonomous system below with the parameters $aneq 0$ and $mn neq 0$:
$$begin{cases}
displaystylefrac{dx}{dt} &=-y+mxy+ny^2\
displaystylefrac{dy}{dt} &=x+ax^2
end{cases}$$
How to prove that there is no periodic orbit in this autonomous system?
I think maybe Dulac's criterion is the tips of this question, but I haven't found the Dulac's Function yet.
differential-equations dynamical-systems
edited Nov 17 at 13:31
Rebellos
12.5k21041
asked Nov 17 at 12:13
panyupj
111
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Consider the autonomous system below with the parameters $aneq 0$ and $mn neq 0$:
$$begin{cases}
displaystylefrac{dx}{dt} &=-y+mxy+ny^2\
displaystylefrac{dy}{dt} &=x+ax^2
end{cases}$$
How to prove that there is no periodic orbit in this autonomous system?
I think maybe Dulac's criterion is the tips of this question, but I haven't found the Dulac's Function yet.
differential-equations dynamical-systems
edited Nov 17 at 13:31
Rebellos
12.5k21041
asked Nov 17 at 12:13
panyupj
111
Consider the autonomous system below with the parameters $aneq 0$ and $mn neq 0$:
$$begin{cases}
displaystylefrac{dx}{dt} &=-y+mxy+ny^2\
displaystylefrac{dy}{dt} &=x+ax^2
end{cases}$$
How to prove that there is no periodic orbit in this autonomous system?
I think maybe Dulac's criterion is the tips of this question, but I haven't found the Dulac's Function yet.
differential-equations dynamical-systems
differential-equations dynamical-systems
edited Nov 17 at 13:31
Rebellos
12.5k21041
asked Nov 17 at 12:13
panyupj
111
edited Nov 17 at 13:31
Rebellos
12.5k21041
asked Nov 17 at 12:13
panyupj
111
edited Nov 17 at 13:31
Rebellos
12.5k21041
edited Nov 17 at 13:31
Rebellos
12.5k21041
edited Nov 17 at 13:31
Rebellos
12.5k21041
12.5k21041
asked Nov 17 at 12:13
panyupj
111
asked Nov 17 at 12:13
panyupj
111
asked Nov 17 at 12:13
panyupj
111
111
add a comment |
add a comment |
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