Questions tagged [nonlinear-system]
In mathematics, a nonlinear system of equations is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one.
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Solutions of a non-linear system
Consider a system of equations $$dd_i=\frac{f}{c}\boldsymbol{v}\cdot\left(\frac{\boldsymbol T}{\|\boldsymbol T\|}-\frac{\boldsymbol T-\boldsymbol p_i}{\|\boldsymbol T-\boldsymbol p_i\|}\right),$$
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Can the Elo update algorithm have multiple stable equilibria?
Let $\Pi$ be a finite set of players. A game on $\Pi$ is a matrix of probabilities $p(i, j)$ for $i, j\in\Pi$ such that $p(i, j) = 1 - p(j, i)$ (we think of $p(i, j)$ as the probability of $i$ beating ...
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Analytically compare the sum of unknowns between two systems of non-linear equations without solving it explicitely
I have two systems of non-linear equations $F(\mathbf{x})=0$ and $G(\mathbf{x})=0,ドル where $\mathbf{x}=[a \quad b\quad c\quad d\quad e\quad f]'\in \mathbb{R}_+^6$. Both of them have a unique solution. ...
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Time constant for system described by a set of nonlinear equations
Suppose we have 2 variables $x$ and $y$ and their relationship is:
Suppose that we have another equation such as $y = dx/dt$ and we want to solve that nonlinear system of equations.
The time ...
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Solve second degree systems of equations
The Problem:
I have the following system of 6 equations of second-degree polynomials in 7 variables ($h$ is known):
$$\begin{equation}
2a(b-e)=1 \\
b^2-e^2+2a(c-f)=0 \\
2(ad+bc-ag-ef)=0 \\
c^2-f^2+2(...
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Stability of 6 by 6 jacobian
I have nonlinear ODE which is
$\frac{d m_{i}}{dt} = \beta\left(\rho + \frac{1}{1+x_{j}^{n}}\right) - m_{i}$
$\frac{d x_{i}}{dt} = \gamma\left(m_{i} - x_{i}\right)$
where $(i, j)=(1,3), (2,1), (3,2)$. ...
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Solving non-linear ODE numerically
I am new to solving non-linear ODEs and I am trying to reproduce the results of section 4 in the paper https://arxiv.org/pdf/1006.2387. The summary of what I am attempting to do is the following.
My ...
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System of non-linear Equations with only 3 saddle points
I am puzzled by a question in my Non-Linear Dynamics lecture. Is there a System of equations of the form $a\in \mathbb{N}, a > 1 $
$$\dot x = x[(x-1)(x+1)]-y$$
$$\dot y = y(1-y^2-ax^2)$$
with only ...