# Tagged Questions

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### Finding the fixed points of a recurrence relation (and systems of) analytically?

How would I go about finding the fixed points of the following recurrence? $$X_n = 2X_{n-1}(2- 3X_{n-1}) + X_{n-1}$$ And therein, determining their stability analytically? Also, how does one find ...
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### Solve the recurrence relation $f(n) = f(n - 1) + f(n - 2) + f(n - 3)$

This is a problem I was playing with that troubled me greatly. $f(n) = f(n - 1) + f(n - 2) + f(n - 3)$ $f(1) = f(2) = 1$ $f(3) = 2$ So, the goal is to try and find a solution for f(n). I tried ...
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### How should I find the analytical form of these recursive equations

I have $$x_1(t+1) = (1-m \rho_1)x_1(t) + n\rho_2 x_2(t) + h1$$ $$x_2(t+1) = (1-m \rho_2)x_2(t) + n\rho_1 x_1(t) + h2$$ Suppose $x_1(0)$ and $x_2(0)$ are known. How can I find the analytical form of ...
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### How to convert this equation into a matrix form

$$F(x)=aF(x-k+1)+bF(x-k+2)+cF(x-k+4)$$ where $F(x)=1$ if $x<k$. $a,b,c,k$ are known (and positive) and $x$ is chosen. I want to solve this recurrence using a matrix but don't really know how to ...
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### How to find fixed point

I have recurrence equations of \begin{align*} x_{n+1} &:= 0.5\cdot (x_{n}^2+2\cdot y_{n}-2\cdot x_{n}\cdot y_{n}-2\cdot y_{n}^2) \\ y_{n+1} &:= -0.8\cdot (x_{n}^2+2\cdot y_{n}-2\cdot ...
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### if $(n+1)c_{n}=nc_{n-1}+2nd_{n-1},d_{n}=2c_{n-1}+d_{n-1}$How prove $c_{n},d_{n}$ are integers

let sequences $c_{n},d_{n}$ such $$c_{0}=0,d_{0}=1$$ and for $n\ge 1$,have $$c_{n}=\dfrac{n}{n+1}c_{n-1}+\dfrac{2n}{n+1}d_{n-1}$$ $$d_{n}=2c_{n-1}+d_{n-1}$$ show that $c_{n},d_{n}$ are integers. my ...
I need to write this recurring system in MATLAB $$x_{n+1}=1-a|x_n|+y_n$$ $$y_{n+1}=bx_n$$ and take its plot for every $x_i,y_i$,with let's say a=1.4 and b=0.7. This is the Lozi map. And this ...
I have the 7 following reccurence relations: $A_n = B_{n-1} + C_{n-1}$ $B_n = A_n + C_{n-1}$ $C_n = B_n + C_{n-1}$ $D_n = E_{n-1} + G_{n-1}$ $E_n = D_n + F_{n-1}$ $F_n = G_n + C_n$ \$G_n = E_n + ...