Mixing
Analyze the stability of the solutions is:
0
$X_{t+1}=1-frac{1}{X_{t} +a+1}$, if $0<a<1$
differential-equations
asked Nov 21 '18 at 18:05
Jhoan LaldrupJhoan Laldrup
172
add a comment |
0
$X_{t+1}=1-frac{1}{X_{t} +a+1}$, if $0<a<1$
differential-equations
asked Nov 21 '18 at 18:05
Jhoan LaldrupJhoan Laldrup
172
1
There is something wrong in your formula, as this does not constitute dynamical system. (It seem me it should be $X_{t+1}=1-frac{1}{X_{t}+a+1}$).
– kolobokish
Nov 21 '18 at 18:08
you're right, I've already put the correct form
– Jhoan Laldrup
Nov 21 '18 at 18:12
1
It seem to me the general solution is of form $X_{n}=1-frac{1}{n+(n-1)*a-frac{1}{X_{0}+a+1}}$ (for some initial $x_{0}$). So to analyze stability you should consider for which values $a$ and $X_{0}$ it converges, for which it not, and for which their is $frac{something}{infty}$ for some $n$.
– kolobokish
Nov 21 '18 at 18:50
add a comment |
0
0
0
$X_{t+1}=1-frac{1}{X_{t} +a+1}$, if $0<a<1$
differential-equations
asked Nov 21 '18 at 18:05
Jhoan LaldrupJhoan Laldrup
172
$X_{t+1}=1-frac{1}{X_{t} +a+1}$, if $0<a<1$
differential-equations
differential-equations
asked Nov 21 '18 at 18:05
Jhoan LaldrupJhoan Laldrup
172
asked Nov 21 '18 at 18:05
Jhoan LaldrupJhoan Laldrup
172
edited Nov 21 '18 at 18:10
Jhoan Laldrup
asked Nov 21 '18 at 18:05
Jhoan LaldrupJhoan Laldrup
172
asked Nov 21 '18 at 18:05
Jhoan LaldrupJhoan Laldrup
172
asked Nov 21 '18 at 18:05
Jhoan LaldrupJhoan Laldrup
172
172
1
There is something wrong in your formula, as this does not constitute dynamical system. (It seem me it should be $X_{t+1}=1-frac{1}{X_{t}+a+1}$).
– kolobokish
Nov 21 '18 at 18:08
you're right, I've already put the correct form
– Jhoan Laldrup
Nov 21 '18 at 18:12
1
It seem to me the general solution is of form $X_{n}=1-frac{1}{n+(n-1)*a-frac{1}{X_{0}+a+1}}$ (for some initial $x_{0}$). So to analyze stability you should consider for which values $a$ and $X_{0}$ it converges, for which it not, and for which their is $frac{something}{infty}$ for some $n$.
– kolobokish
Nov 21 '18 at 18:50
add a comment |
1
There is something wrong in your formula, as this does not constitute dynamical system. (It seem me it should be $X_{t+1}=1-frac{1}{X_{t}+a+1}$).
– kolobokish
Nov 21 '18 at 18:08
you're right, I've already put the correct form
– Jhoan Laldrup
Nov 21 '18 at 18:12
1
It seem to me the general solution is of form $X_{n}=1-frac{1}{n+(n-1)*a-frac{1}{X_{0}+a+1}}$ (for some initial $x_{0}$). So to analyze stability you should consider for which values $a$ and $X_{0}$ it converges, for which it not, and for which their is $frac{something}{infty}$ for some $n$.
– kolobokish
Nov 21 '18 at 18:50
1
1
There is something wrong in your formula, as this does not constitute dynamical system. (It seem me it should be $X_{t+1}=1-frac{1}{X_{t}+a+1}$).
– kolobokish
Nov 21 '18 at 18:08
There is something wrong in your formula, as this does not constitute dynamical system. (It seem me it should be $X_{t+1}=1-frac{1}{X_{t}+a+1}$).
– kolobokish
Nov 21 '18 at 18:08
you're right, I've already put the correct form
– Jhoan Laldrup
Nov 21 '18 at 18:12
you're right, I've already put the correct form
– Jhoan Laldrup
Nov 21 '18 at 18:12
1
1
It seem to me the general solution is of form $X_{n}=1-frac{1}{n+(n-1)*a-frac{1}{X_{0}+a+1}}$ (for some initial $x_{0}$). So to analyze stability you should consider for which values $a$ and $X_{0}$ it converges, for which it not, and for which their is $frac{something}{infty}$ for some $n$.
– kolobokish
Nov 21 '18 at 18:50
It seem to me the general solution is of form $X_{n}=1-frac{1}{n+(n-1)*a-frac{1}{X_{0}+a+1}}$ (for some initial $x_{0}$). So to analyze stability you should consider for which values $a$ and $X_{0}$ it converges, for which it not, and for which their is $frac{something}{infty}$ for some $n$.
– kolobokish
Nov 21 '18 at 18:50
add a comment |
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1
There is something wrong in your formula, as this does not constitute dynamical system. (It seem me it should be $X_{t+1}=1-frac{1}{X_{t}+a+1}$).
– kolobokish
Nov 21 '18 at 18:08
you're right, I've already put the correct form
– Jhoan Laldrup
Nov 21 '18 at 18:12
1
It seem to me the general solution is of form $X_{n}=1-frac{1}{n+(n-1)*a-frac{1}{X_{0}+a+1}}$ (for some initial $x_{0}$). So to analyze stability you should consider for which values $a$ and $X_{0}$ it converges, for which it not, and for which their is $frac{something}{infty}$ for some $n$.
– kolobokish
Nov 21 '18 at 18:50