For what values of the parameter $c$ the difference equation have periodic (2-cycle) solutions
up vote
0
down vote
favorite
I have difference equation:
$y(n+1)=y(n)^2+c$
At what value of parametr $c$ the equation have a 2-cycle solution?
In this example $f(y)=y^2+c$
To solve the problem, I wanted to solve this equation: $y=f(f(y))$ because solution of the equation is periodic 2-cycle.
i got the roots of this equation:
$y_1=frac{1}2(-sqrt{-4c-3}-1)$
$y_2=frac{1}2(sqrt{-4c-3}-1)$
$y_3=frac{1}2(-sqrt{1-4c}+1)$
$y_4=frac{1}2(sqrt{1-4c}+1)$
but I don't know what to do next. How to find the necessary parameter values using the roots?
differential-equations
asked Nov 18 at 18:21
bvl
72
add a comment |
up vote
0
down vote
favorite
I have difference equation:
$y(n+1)=y(n)^2+c$
At what value of parametr $c$ the equation have a 2-cycle solution?
In this example $f(y)=y^2+c$
To solve the problem, I wanted to solve this equation: $y=f(f(y))$ because solution of the equation is periodic 2-cycle.
i got the roots of this equation:
$y_1=frac{1}2(-sqrt{-4c-3}-1)$
$y_2=frac{1}2(sqrt{-4c-3}-1)$
$y_3=frac{1}2(-sqrt{1-4c}+1)$
$y_4=frac{1}2(sqrt{1-4c}+1)$
but I don't know what to do next. How to find the necessary parameter values using the roots?
differential-equations
asked Nov 18 at 18:21
bvl
72
This is a difference equation not a differential equation.
– Anurag A
Nov 18 at 18:28
thank you, i fixed.
– bvl
Nov 18 at 18:31
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have difference equation:
$y(n+1)=y(n)^2+c$
At what value of parametr $c$ the equation have a 2-cycle solution?
In this example $f(y)=y^2+c$
To solve the problem, I wanted to solve this equation: $y=f(f(y))$ because solution of the equation is periodic 2-cycle.
i got the roots of this equation:
$y_1=frac{1}2(-sqrt{-4c-3}-1)$
$y_2=frac{1}2(sqrt{-4c-3}-1)$
$y_3=frac{1}2(-sqrt{1-4c}+1)$
$y_4=frac{1}2(sqrt{1-4c}+1)$
but I don't know what to do next. How to find the necessary parameter values using the roots?
differential-equations
asked Nov 18 at 18:21
bvl
72
I have difference equation:
$y(n+1)=y(n)^2+c$
At what value of parametr $c$ the equation have a 2-cycle solution?
In this example $f(y)=y^2+c$
To solve the problem, I wanted to solve this equation: $y=f(f(y))$ because solution of the equation is periodic 2-cycle.
i got the roots of this equation:
$y_1=frac{1}2(-sqrt{-4c-3}-1)$
$y_2=frac{1}2(sqrt{-4c-3}-1)$
$y_3=frac{1}2(-sqrt{1-4c}+1)$
$y_4=frac{1}2(sqrt{1-4c}+1)$
but I don't know what to do next. How to find the necessary parameter values using the roots?
differential-equations
differential-equations
asked Nov 18 at 18:21
bvl
72
asked Nov 18 at 18:21
bvl
72
edited Nov 18 at 20:48
asked Nov 18 at 18:21
bvl
72
asked Nov 18 at 18:21
bvl
72
asked Nov 18 at 18:21
bvl
72
72
This is a difference equation not a differential equation.
– Anurag A
Nov 18 at 18:28
thank you, i fixed.
– bvl
Nov 18 at 18:31
add a comment |
This is a difference equation not a differential equation.
– Anurag A
Nov 18 at 18:28
thank you, i fixed.
– bvl
Nov 18 at 18:31
This is a difference equation not a differential equation.
– Anurag A
Nov 18 at 18:28
This is a difference equation not a differential equation.
– Anurag A
Nov 18 at 18:28
thank you, i fixed.
– bvl
Nov 18 at 18:31
thank you, i fixed.
– bvl
Nov 18 at 18:31
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3003912%2ffor-what-values-of-the-parameter-c-the-difference-equation-have-periodic-2-cy%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
This is a difference equation not a differential equation.
– Anurag A
Nov 18 at 18:28
thank you, i fixed.
– bvl
Nov 18 at 18:31