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Questions tagged [nonlinear]

Used to mark questions about nonlinear differential equations, `NonlinearModelFit`, and related to nonlinear dynamics.

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Transform a set of nonlinear equations in state space form

I have to solve a multi-body dynamic problem numerically in Matlab. The set of equations has been computed in Mathematica. To solve it in Matlab i have to transform it into state space representation. ...
Marilace's user avatar
0 votes
1 answer
76 views

Using NonlinearModelFit for fitting equation with two variables and 6 or more Parameters

In the original question posted on 23-04-2024, there was a typo in the numbers given in the nested lists: a superscript symbol (^) was missing in the nested list, i.e, it should have been $9.62948*10^{...
sreeraj t's user avatar
  • 303
2 votes
2 answers
140 views

Problems with code to solve nonlinear ODE applied to BEC

Strictly I must solve my problem with an asymptotic approximation carried out by the series method. The code I have made is the following to solve my problem $$ R''(s) + \frac{1}{s}R'(s) - \frac{1}{s^...
Litafie's user avatar
  • 33
5 votes
2 answers
169 views

Regarding phase space diagram/trajectory

I have a 3D chaotic system and its one 3D phase-space portrait and three 2D phase-space portrait (x-y plane, y-z plane, z-x plane) are given below. ...
Arssat's user avatar
  • 91
0 votes
2 answers
107 views

NonlinearModelFit extremely slow performance with a single iteration

I have been experiencing very slow performance of NonlinearModelFit. The code that in my case causes that is below. The first part gets the data, the model and ...
atapaka's user avatar
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2 votes
1 answer
136 views

Bifurcation Analysis and Lyapunov Exponents Visualization [closed]

...
Athanasios Paraskevopoulos's user avatar
2 votes
2 answers
220 views

Phase response curve

I just want to plot the phase response curve (phase vs. frequency curve) for the following nonlinear differential equation: ...
Champ92's user avatar
  • 23
0 votes
0 answers
104 views

Fitting problem for sigmoid like experimental data

I have data like this ...
rani's user avatar
  • 343
8 votes
3 answers
532 views

Basins of attraction using Newton-Raphson method for nonlinear system

I am trying to construct basins of attraction using the newton's method for the system of two equations whose roots are real. I need to develop a code to get basin of attraction. Unfortunately, my ...
onk's user avatar
  • 119
2 votes
1 answer
138 views

Bifurcation Diagram for x' = (rx) - sinx

I solved for finding the fixed points analytically for various ranges of u for x'[t] = (ux) - sinx for u = 0 0 <u <<1 u>1 0>u>-infinity and its a very complicated bifurcation ...
CuriousMind's user avatar
0 votes
1 answer
137 views

How to solve and analyze a system of 15 equations with 15 variables?

I have a system of $15$ equations and $15$ key variables. Some of the equations are non-linear. Some constant variables in the equation can be equal to numbers to solve the system. I have to find a ...
Moi's user avatar
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0 votes
1 answer
127 views

Is it possible to make a phase portrait of this system?

I need help with this problem: I have this ODE system For this system, manually, I calculated the stability points, eigenvalues, and Jacobian matrix for a range of ALPHA values (I considered those ...
Victor Pinto Msc Student's user avatar
2 votes
1 answer
138 views

Consumer Maximization Problem Doesn't Work in Wolfram Mathematica

I'm trying to solve a problem that can be seen in the paper "The Role of the Structural Transformation in Aggregate Productivity". The problem is: Manually it is difficult to find the ...
mjr's user avatar
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1 vote
0 answers
54 views

My sinusoidal fit requires an unused extra constant to work

I am trying to fit a sinusoidal curve onto the following data: ...
Zeke Coady's user avatar
0 votes
0 answers
58 views

NDSolve does not accept the boundary condition

I am new at Mathematica and trying to solve a nonlinear PDE with the help of NDSolve. H, the height of the current is a function of x and t. Based on the context I know the current has a parabolic ...
AWer's user avatar
  • 35
0 votes
1 answer
135 views

How to Plot the Steady State Phase Response Curve?

I have a code to plot the steady state frequency response curve (provided by @ Michael E2), How can I plot the steady state phase response with the help of this code same as shown in the figure: . <...
Abhishek 's user avatar
1 vote
1 answer
81 views

Insert a nonlinear PDE in Mathematica

I am new to Mathematica and trying to learn its language. I want to solve a non-linear PDE but don't know how to insert it. Would you please help me or give me some tutorial about it?
AWer's user avatar
  • 35
2 votes
2 answers
149 views

Graph of a 3D discrete-time dynamical system

I have a set of difference equations defining a 3D dynamical system with specific parameter values. How can I create a 3D phase portrait to display its trajectories and identify potential attractors? $...
Zafar Boxonov's user avatar
2 votes
1 answer
116 views

Why NDSolve can not solve this second-order nonlinear ODE

I try to solve: eq[t_] := ddf[t] + a'[t]/a[t] df[t] + 6 f[t] - 3 a[t]^2 f[t]^2 with ...
Dr. phy's user avatar
  • 287
2 votes
2 answers
99 views

Series and Numerical Solution of Second Order Boundary Value Problem using Mathematica

I am just a toddler in Mathematica, please help me in finding the numerical and series solution of the following boundary value problem: u''[t] == - A u[t]^4, u[0]==1, u[1]==1, where A lies in ...
Manish Jain's user avatar
3 votes
1 answer
114 views

NDEigensystem does not work when using nonlinear operator [closed]

I am trying to find the eigenvalues of the stationary Gross Pitaevskii equation using the NDEigensystem command via ...
user3623974's user avatar
3 votes
1 answer
203 views

How to create an interactive Poincare section from the given code?

Here we discussed Poincare section for perturbed string model taken from the paper Chaotic dynamics of a suspended string in a gravitational background with magnetic field. We try to reproduce some ...
codebpr's user avatar
  • 2,263
3 votes
2 answers
241 views

How can I solve this system of nonlinear PDEs?

How can I solve these PDE analytically for $z$ and $y$? \begin{eqnarray} 2 \dot{z} &=& \ddot{y}+ y^{-1}, ~~~ (1)\\ z' + \dot{z}' &=& - \dot{y}'. ~~~~~~~~~~ (2) \end{eqnarray} Where (....
Dr. phy's user avatar
  • 287
1 vote
0 answers
48 views

Extracting singularity or stiff point from NDSolve [duplicate]

Given the coupled non-linear differential equations: ...
Daniel Vainshtein's user avatar
2 votes
3 answers
202 views

Are there exact solutions for the following system of nonlinear first order ordinary differential equations?

The two equations are: u'[t]== -(K + L v[t]) u[t] and v'[t] == -L u[t] v[t] where K and L are constants. At t=0, u(0)=a ...
TNEst's user avatar
  • 21
3 votes
1 answer
199 views

How to find a unimodular integer matrix $T$ satisfying $T^\top A T=B$ given symmetric integer matrices $A,B$?

Given two unimodular symmetric integer matrices $A$ and $B$, I asked how to find a unimodular integer $T$ that satisfies this nonlinear relation between $T$ and $A,B$ like this in Mathematica: ...
zeta's user avatar
  • 251
3 votes
2 answers
204 views

Meaning of arguments in FittedModels`ParameterEllipsoid

I am trying to figure out what FittedModels`ParameterEllipsoid's parameters mean (I want to construct a filled ellipse) Here is a minimum working example: ...
Craig Carter's user avatar
  • 4,510
8 votes
2 answers
388 views

Given square matrices A and B, how to solve T obeys Transpose[T]. A . T = B?

Dear Mathematica experts, Given two square matrices, A and B, how do we use Mathematica to solve a matrix T such that T satisfies this matrix equation? (Here we have A,B,T $\in$ general linear matrix ...
zeta's user avatar
  • 251
1 vote
1 answer
346 views

Fitting delay differential equations (DDE)

I have the following differential equations: $$S'(t) = 0.31 S(t) \Big( 1 - \frac{S(t)}{6.19} \Big)- \frac{a}{1 + B(t)} S(t),$$ $$B'(t) = c (1 - B(t)) - d B(t) S(t) - 3 c (1 - B(t - 18)),$$ where $B(t -...
user avatar
4 votes
2 answers
199 views

Nonlinear model fit not working

Probably a very simple fix, but I'm trying to fit a simple exponential. Even when I put in good guesses, the model won't fit the data. Any suggestions? ...
icebox207's user avatar
  • 131
1 vote
1 answer
72 views

Extract boundary points of an interpolating function obtained by NDSolve

Given a set of coupled nonlinear equations I want to extract the boundary points that appears in the interpolation function obtained as an output to NDSolve function and then to define them directly ...
Daniel Vainshtein's user avatar
0 votes
0 answers
40 views

Trouble implementing switching hybrid system with NDSolve

I'm trying to use NDSolve to simulate a hybrid nonlinear system that switches between different linear behaviors based on states and inputs (i.e. switching from one linear behavior to another) which ...
Cameron Alred's user avatar
1 vote
0 answers
463 views

How to include impulses in differential equations?

I have two coupled differential equations as follows: $$S'(t) = - \frac{a}{1 + B(t)} S(t),$$ $$B'(t) = \frac{c}{1 + S(t)} B(t) (1 - B(t)) - d B^2(t) \Big( \frac{1 - B(t)}{B(t)} \Big)^n,$$ where $a$, $...
user avatar
2 votes
1 answer
52 views

How to linearize these terms in many different variables? [duplicate]

How to linearize these terms in q[t] and p[t,y] ...
Dr. phy's user avatar
  • 287
0 votes
1 answer
200 views

Using ParametricNDSolveValue and MultiNonlinearModelFit to fit an ODE system to datasets

I asked a question here about fitting an ODE system to given datasets. The great answer of @ydd solved the problem nicely. In the mentioned answer, the initial values are taken as the initial points ...
user avatar
4 votes
2 answers
426 views

Modeling experimental data with differential equations

I have the following two sets of experimental data, which show the dependencies of two quantities, namely, $S$ and $B$, on time ($0$ h, $3$ h, $6$ h, $9$ h, $15$ h, $18$ h, $21$ h, and $24$ h): ...
user avatar
0 votes
1 answer
63 views

How to linearize this equation in two different variables?

How to linearize this equation in two different variables p[t] and q[t,y]: ...
Dr. phy's user avatar
  • 287
3 votes
1 answer
127 views

How to optimize ODE parameter fitting?

Consider the data ...
sam wolfe's user avatar
  • 4,863
1 vote
1 answer
57 views

How to fit a linear ODE system?

Consider the equations $$ \begin{align} b'(t)=p_1 c(t)-k_1b(t),\\ c'(t)=p_2b(t)-k_2c(t) \end{align} $$ Given data on $b$ and $c$, and initial conditions, how do I find the best fitting parameters $k_1,...
sam wolfe's user avatar
  • 4,863
2 votes
0 answers
63 views

NonlinearModelFit of data with errors

Experimental data points invariably come with errors. These errors can significantly influence the parameters and their uncertainties when performing non-linear fitting. However, NonlinearModelFit ...
Филипп Цветков's user avatar
0 votes
2 answers
146 views

Fitting data with ${\rm sinc}^2(x)$

I performed an experiment of Fraunhofer diffraction with slits, the results of which should be proportional to $\operatorname{sinc}^2(x) = \left(\frac{\sin x}{x}\right)^2$. However, an error occurred ...
L0wc3ll's user avatar
1 vote
0 answers
90 views

Problem to solve computationaly and plot the phase portrait of a nonlinear ode system

I am here again to see if some one can help me. This time, I have problem to solve, computationally and plot the phase portrait of a nonlinear ode system (The Duffing Equation with just the spring ...
Victor Pinto Msc Student's user avatar
0 votes
0 answers
83 views

Time independent perturbation theory for solving coupled differential equations

The eqexact1 and eqexact2 are the coupled differential equation of motion with g lets say a repulsive factor, that I choose. ...
Pantelis Ashikkis's user avatar
1 vote
1 answer
94 views

Simultaneous NonlinearModelFit for two data sets that are separate functions of x and t [duplicate]

I am trying to simultaneously fit two data sets that are separate functions of $x$ and $t$ with NonlinearModelFit. Here is an example of the data: ...
sje1g13's user avatar
  • 45
0 votes
1 answer
86 views

Solving differential equation with hyperbolic functions

I've been trying to solve the following differential equation: \begin{equation}\left( \frac{d \tau}{d \sigma} \right)^2 = \frac{(E_0 \cosh\sigma-p_\tau\sinh\sigma)^2}{(E_0 \cosh\sigma-p_\tau\sinh\...
MarcelRomp's user avatar
1 vote
2 answers
78 views

Fitting linear decay to a semilogarithmic line

I am trying to fit this set of data,I tried a simple linear model but it didn't yield successful results, I also tried curve_fit on Python but also no luck - here ...
atomic-muclei's user avatar
0 votes
2 answers
93 views

Set of differential equations with trigonometric functions and a derivative squared

I've been trying to solve a set of differential equations that involve the square of a derivative, similar to another post I made here, and trigonometric functions, as seen here \begin{equation} \frac{...
MarcelRomp's user avatar
4 votes
2 answers
463 views

Solving coupled differential equations involving the square of the derivative

I want to solve the following system of coupled differential equations in order to obtain particle trajectories: \begin{equation} \frac{dt}{ds} = (E-y\, p_t)y \end{equation} \begin{equation} \...
MarcelRomp's user avatar
1 vote
1 answer
133 views

Nonlinear experimental data fit without initial parameters

I am trying to fit correlation data into a non-linear model but it is not working. My data plot looks like this: The equation I am using for fit is The Mathematica script i am using looks like: <...
SKR's user avatar
  • 11
1 vote
0 answers
48 views

WhenEvent in ParametricNDSolve but not executed

I tried to solve a partial differential equation with parameters, the critical condition of which I used WhenEvent to express, but the solution after bringing in the parameters shows that the ...
Wd Wd's user avatar
  • 11

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