Questions tagged [difference-equations]

Tag for the usage of RSolve, RecurrenceTable, DifferenceRoot, and other functions related to difference equations.

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Bifurcation diagram for coupled nonlinear difference equations

I’ve been trying to plot bifurcation diagram of 2D map for this system $x_{t+1} = x_t + y_t + A x_t y_t - b x_t$ $y_{t+1} = y_t + \dfrac{x_t}{A} - x_t y_t + c y_t^2 - d y_t$ From example by Chris K in ...
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2answers
134 views

eigenvalue and eigenfunction of complex euler-bernoulli beam

So I am new to Mathematica and am trying to solve the euler-bernoulli modal equation for a U-shaped Cantilever beam given by equations :- where i is the index of the region. In total there are 2 ...
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1answer
185 views

How do I use RSolve to solve the problem below?

RSolve can't compute the solution. Appears that Mathematica is having a convergence problem. I don't know if the boundary conditions are properly defined... ...
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1answer
51 views

A modular version of LinearRecurrence?

I'm playing around with implementing the Lucas probable prime test (mainly so I can understand it better), and would love a version of the LinearRecurrence function that used addition modulo n (with n ...
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0answers
31 views

Parametrization of twisted pseudospheres types 2 and 3

Among the three types of rotationally symmetric Pseudospherical surfaces $K=-1$ (Beltrami central, type 2 and type 3) (http://xahlee.info/surface/gallery.html) we have Dini twist addition term $ b\...
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3answers
123 views

Nonlinear Difference Equations [closed]

How can I plot the nonlinear difference equations?
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1answer
29 views

Why does DifferenceRoot evaluate only in this table?

I would like to use a complicated function containing DifferenceRoot as a replacement rule, but somehow it evaluates only in ...
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1answer
49 views
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0answers
27 views

Solve ODE transformed into q-difference in Mathematica

Let's take a simple differential equation: $\frac{dx}{dt} = -x(t)$ Suppose we want to do a q-transform. To do this, we will replace the time derivative $\frac{d}{dt}$ with the q-derivative (also known ...
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1answer
88 views

How I can plot the below map?

I have tried to plot the following map: $\qquad \begin{cases} y_{n+1}=r y_n^{x_{n+1}-x_{n+2}}\\ y_1=x_1-x_2 \quad \end{cases}$ using the code shown below. The error I have got is that x[1] - x[2] ...
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2answers
80 views

Plot linear difference equations

How can I plot an unstable node, saddle, and center in linear two-dimensional difference equations? I can plot the stable node, please see the code. Thank you in advance. ...
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35 views

Solving a difference equation involving summation expressions-Implicit output

I am trying to solve a difference equation involving summation expression with the following code: ...
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1answer
277 views

Find RSolve solution reflecting special structure of DifferenceRoot[Function[{\[FormalY], \[FormalN]}

RSolve yields a large (multi-page) solution (LeafCount=25891) containing a number of 7F6 (and higher) hypergeometric functions when applied to ...
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36 views

How to study convergence of recurrence relations?

Is there a way to test the convergence of a recurrence relation in Mathematica? For example does this relation converge: $$a_{n+1}=a_n \dfrac{n-\dfrac{1}{4}+c^2}{-5+5c^2}$$ for some values of the ...
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1answer
72 views

How to solve this recurrence equation with Mathematica?

I am interested in solving this recurrence relation (equation) with Mathematica code. I am new to Mathematica. I tried RSolve, RSolveValue, AsymptoticRSolveValue commands for this. But I am not ...
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3answers
209 views

Problem plotting a bifurcation diagram of logistic map

I would like to plot a bifurcation diagram from the logistic map (difference equation) of the type $$ x_{t+1} = r\,(1-x_{t})\,x_{t}. $$ The code I used for that was ...
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1answer
49 views

Making change of variable

I have the following expression $$L=\frac{m}{2}\left(\dot{q}^{2} \sin ^{2} A t+\dot{q} q A \sin (2A t)+q^{2} A^{2}\right)$$ with $q=q(t)$ I want to make a change of variabl $$Q=q\sin(At)$$ By hand I ...
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1answer
117 views

Solve 2D Difference Equations

If I have a system of difference equations $$ \begin{cases} x(n + 1) = x(n) + x(n) y(n) + y(n)^2 \\ y(n + 1) = y(n) - x(n)^2 + y(n)^2 \end{cases}, \text{ with } \begin{cases} x(0) = 1\\ y(0) = 2 \end{...
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1answer
57 views

Plot system difference equations

Is this way correct to plot system of difference equation. For example ...
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1answer
73 views

How to plot the roots of two complex equations?

I have these two equations as two variables '$a1$' and '$b1$', mentioned below and I want to plot the roots of $a1^{\dagger}*a1$ with respect to P0, which will give me bistable plot with three values. ...
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2answers
152 views

How can I find the coefficients of the next recursive symbolic function?

I have the following function $$ f(x+3k) = -mf(x+2k)+f(x) $$. If we get $x=x+k$, then $$ f(x+4k) = -mf(x+3k)+f(x+k) = m^2f(x+2k)+f(x+k)-mf(x) $$. Also we obtain the coefficients of the final functions,...
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1answer
93 views

Phase portrait for three dimensional system of nonlinear difference equation using Mathematica

I am a student of M.Phil Mathematics. I am working on a non linear system of difference equations in three dimensions. I want to draw a phase portrait for my system using Mathematica. I was trying ...
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4answers
228 views

Generate a random Fibonacci sequence

I want to generate the random sequence defined by $a_n = a_{n-2} + \beta(n)a_{n-1}$ where $\beta$ takes the values $\pm1$. My attempt is: ...
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3answers
81 views

What is the fastest way to calculate series from recurrence solutions with no closed form?

I am not very experienced with Mathematica. I want to calculate the series from recurrence solutions. These solutions have no closed-form. I want to improve the approximation and hence need a good ...
3
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1answer
162 views

MAP a business cycles model

There is a Business Cycles Map on Phaser 3.0 and I've trying to run it on Mathematica the last four days without succes. The equations are $$ x_1 = (1.0 - a s)x_1 + a \left[s m + g \left(\frac{s m}{...
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1answer
54 views

difference equation and continued fractions

I'm interested in solving the following difference equation: $x[k-1]+(k^2+k+a)/x[k]=b$, $k=1,2,\ldots$, where $a,b$ are fixed positive numbers; let's say $x[1]=c>0$. Mathematica's ...
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2answers
121 views

Using RSolve for recurrence equation

I'd like to use Mathematica to verify the solution to a recurrence equation. I have the following equation: $Q_{k+1} = Q_k + \alpha(r_{k+1} - Q_k)$. I also have a derivation showing how to obtain a ...
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2answers
136 views

Counting the number of binary strings of length m with no consecutive 1s (RR). How to improve it?

I am new to Mathematica and I am trying to solve this problem of counting the number of binary strings of a certain length m, as far as no consecutive 1s are there. For instance m = 3, my recurrence ...
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38 views
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72 views

Plot a stable 4-periodic orbit

I have a question guys In Mathematica how I can plot a stable 4-periodic orbit in the logistic map with giving the four x values for the orbit and find the a value for which it goes through a period ...
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1answer
37 views

How to use elements of tables in recurrence tables?

I am trying to use a List inside a RecurrenceTable. Suppose I have the list ...
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2answers
258 views

Find a stable 3-cycle of the sine map

I am trying to find an stable 3-cycle for the sine map $g(x) = a \sin(\pi x)$ but I do not know exactly how to use mathematica to do so. Is there anyone familiar with this? $x$ lies as before ...
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2answers
72 views

Trying to generate strings using Recurrence Table

I'm trying to generate strings recursively that look like this: ...
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1answer
343 views

Finite Difference - heat generation in a square (square within a square)

I am trying to develop a code that will allow me to solve the following problem. Lets say that I have a square block, inside that square block I have a smaller square box thats at a certain ...
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0answers
66 views

Dirac Operator in de Sitter background

I am attempting to write the Dirac operator in a curved background, and eventually solve the equation as a second order PDE, since I am attempting to bring it into Klein-Gordon form. Essentially what ...
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1answer
54 views

Problem in table [duplicate]

NDSolve[{t,Evaluate[{ode}\.Sol]},{t,0,10,1}]//TableForm After executing this with appropriate equations I get solution in the tabular form but when I try to ...
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2answers
302 views

How to plot a system of recurrence equations

I have the following code working well ... but I would then like to plot M[k] and L[k] on the same axes with k along the horizontal and M[k] and L[k] values along the vertical. The graph I'm looking ...
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0answers
52 views

plot discrete system by mathematica

if I have a discrete system x(n+1)= 0+y , y(n+1)= -0.5x +0 The fixed point (0,0) is center by Jacobian., I do not know how Plot this by using Mathematica code to get center. I am thankful if any one ...
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1answer
79 views

How do I create a bifurcation diagram for the below iterative map? [closed]

I have tried to create a bifurcation diagram for the following iterative map: x[n+1]=-r Log x[n], x[1]=0.711 and r=1/log(n(n+1)) using the following code But it doesn't work. Any help? ...
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0answers
33 views

How to apply RecurrenceTable or Array in two dimensions

This question relates to 104959. How can I solve the following (akward) code by using RecurrenceTable or Array? ...
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1answer
92 views

Plot 2-D system difference equations

If I have 2-D system difference equations x(n+1)=x(n)-5y(n) , y(n+1)= 2x(n)+y(n) I need to plot this system. I did : ...
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0answers
68 views

Compute the sum given a recursion for each summand

I have a system of two recursive equations with two unknowns A[n] and B[n] which apparently Mathematica can't solve RSolve not ...
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47 views

Nest function n times

A trivial example would be f[x_]:=x Nest[f, 7, n] which would of course be 7 because it is independent of ...
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0answers
40 views

RSolve not evaluating when given my system of recurrence equations

I am trying to solve the following system of recurrences with RSolve: ...
3
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4answers
90 views

RecurrenceTable for systems of linear difference equations

I'm working on a project that involves developing a financial forecasting model. The equations used in the model will largely be linear difference equations (estimated via some form of regression ...
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2answers
319 views

Periodic Orbits of the MacKay Map

For the MacKay (Henon action-angle transformation) Map (Mackay 1983): $x_{n+1}=q-\alpha x_n-x_n^2-y_n \\ y_{n+1}=x_n$ with $q, \alpha \in \mathbb{R}$ real parameters I would like to calculate the ...
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0answers
35 views

RecurrenceTable doesn't evaluate with constant right-hand side

One of my functions automatically generates systems for RecurrenceTable. Usually works fine, but today I encountered a problem. If the right-hand side is a ...
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147 views
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25 views

Issue plotting a system of recurrence equations

Mathematica noob issues here. So I've got a system of recurrence equations, and following suggestions in other posts,(Plotting two recursive functions) I have the following: ...
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0answers
29 views

RSolve produces a solution which is not complete?

Consider the following solution of a recurrence relation in two variables RSolve[f[x + 1, y] == f[x, y + 1], f[x, y], {x, y}] {{f[x, y] -> C[1][x + y]}} It ...

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