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Questions tagged [stability]

The tag has no usage guidance.

1
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1answer
80 views

Plot a Mathieu stability chart

I'm working with the Mathieu equation as a part of my research and as part of the analysis I'd like to include a stability chart such as Fig. 1 in this paper. Unfortunately I'm stuck with Mathematica ...
0
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1answer
32 views

Why SVD cannot recover the original matrix and suffer from numerical instability? [closed]

I have a matrix in mathematica that looks like $m= \left( \begin{array}{cccc} -i & 0 & 1 & 0 \\ 0 & -i & 0 & -1 \\ 1 & 0 & -i & 0 \\ 0 & -1 & 0 & -...
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0answers
36 views

Removing numerical instability in plots of functions over large domains

suppose you have a large domain you wish to plot a function over, which depends on numerical values usually around or above you machine precision e.g. ...
1
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2answers
38 views

Diagnosing the numerical stability of a function

I have programmed a function f[x] that seems to be very unstable numerically. More precisely, I noticed that for certain arguments in arbitrary precision, the ...
2
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1answer
77 views

Stochastic Mathieu equation: Is this a numerical instability?

So I am a beginner with stochastic differential equations and came across Mathematica's capabilities for solving them. I am solving the stochastic Mathieu equation with a harmonic forcing term that ...
0
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0answers
93 views

Linear Stability Analysis of dynamical system

I'm starting to use Mathematica for some linear stability analysis of a discrete non-linear dynamical system. I can't find an on-line tutorial for it, and I'm quite at a loss (in fact I can't even ...
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0answers
75 views

Adding a perturbation to a dynamic 3-tier food chain model

I have a predator prey food chain model set up as follows, with x representing the resource, y the consumer, and z the predator: ...
0
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0answers
55 views

Difficulty plotting a null cline [duplicate]

Problem Statement Pplane produces this phase plane portrait: Note the yellow line which represents the locus where $\dot{y}=0$. My attempts to recreate this plot in Mathematica have failed. The ...
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0answers
138 views

Lyapunov exponent and stability of limit cycles

I have a four dimensional dynamical system where I have a Hopf bifurcation. My aim is to figure out if limit cycles are stable or not. The calibration in the system is ...
0
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1answer
170 views

Combining gradient color schemes on a ContourPlot [duplicate]

Starting point Function of interest: $$ f(x,y)=-\frac{2 x^5+x y+2 y^7}{x^2+y^2} $$ f[x_, y_] = -((2 x^5 + x y + 2 y^7)/(x^2 + y^2)) ContourPlot: ...
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1answer
554 views

Solving system of ODE and Equilibrium points

This is the first time I am using Mathematica and I am trying to solve the system of ODE, $\dot x=x(1-x)-\frac{2xy}{y+x}\qquad\dot y=-1.5y+\frac{2xy}{y+x}$ When I used ...
1
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1answer
122 views

Nonlinear 2nd order ODE with regular singularities

I am tring to solve the following ODE with NDsolve $2x~(1-x)~f''(x)+(3-4x)~f'(x)+a~f(x)+b~f^n(x)=0;~~a,b\in\mathbb{R},~n\in\mathbb{N}$. The mathematica "code" is: ...
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0answers
103 views

Improving numerical stability of the Goldstein-Price Function

Goldstein-Price Function is a two-dimensional test function for optimization, defined as $$f(y,z) = \left(\left(3 y^2+2 y (3 z-7)+z (3 z-14)+19\right) (y+z+1)^2+1\right) \times \left(\left(12 y^2-4 y (...
3
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0answers
266 views

Stability analysis of transcendental equation (stability crossing curves)

I am working with a non-linear delay system with three scalar delays. After taking the Laplace transform of the linearized system, the characteristic function is a transcendental equation with three ...
3
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1answer
1k views

Stability Boundaries via Routh-Hurwitz Criterion

I'm attempting to determine the stability boundaries of a 2nd order system via Routh-Hurwitz stability criterion. That is to say, I need to compute when a polynomial, which is in terms of variables "a"...
8
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3answers
871 views

How to prevent instability blow up in NDSolve?

I have the following code to solve a PDE: ...
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0answers
442 views

Stability region of midpoint method using Solve and RegionPlot

I've been trying to obtain the stability region in the $(\lambda_R, i\lambda_I)$ plane of the midpoint rule $$y_{n+1}= y_{n-1}+2h\dot{y}_n,$$ for the model problem $\dot{y}=\lambda y$. The roots for ...
1
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1answer
98 views

How to make a discretized NMinimize more precise

I am using Mathematica for physics research and I want to minimize a Hamiltonian equation with respect to two variables (I have also discretized the problem). I have a single constraint. When I plot ...
2
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1answer
1k views

How to plot the Euler's formula in 3D?

In Von Neumann's stability analysis of Finite Difference Equations, the Euler's formula is used to describe a perturbation. Now the finite difference equation is stable if this perturbation does not ...
4
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1answer
408 views

How to demonstrate lack of stability with advection equation

I am trying to that using a coarse grid with an explicit method for, say, the advection equation leads to an unstable solution. The trouble is Mathematica avoids unstable solutions with good ...