Questions tagged [nonlinear-system]

Question 1

Consider a system of equations $$dd_i=\frac{f}{c}\boldsymbol{v}\cdot\left(\frac{\boldsymbol T}{\|\boldsymbol T\|}-\frac{\boldsymbol T-\boldsymbol p_i}{\|\boldsymbol T-\boldsymbol p_i\|}\right),$$ ...

Question 2

As a premise, this question is mainly out of curiosity, and to look for some references regarding this systems. Case $\bf n=2$ Let $f(x,y)=e^{x+y}+e^x+e^y$ and suppose we want to solve the following ...

Question 3

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 ...

Question 4

Consider the definition of $R$-convergence as given in Definition 9.2.1 of "Iterative solutions of nonlinear equations in several variables" by Ortega and Rheinbolt. Let $A$ be a fixed-...

Question 5

I have two systems of non-linear equations $F(\mathbf{x})=0$ and $G(\mathbf{x})=0$, 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. ...

Question 6

I want to model the flight of a ball. For this I want to consider air resistance, Magnums force and of course gravity. For simplification $\omega$, the rotational speed, is constant. Furthermore the ...

Question 7

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 ...

Question 8

Note. I know that this non-linear differential equation is generalized in other posts. I wanted to check my proof, different from others. $f’(x)=c^2-\{f(x)\}^2, \ c>0, \ f: \Bbb{R}\to\Bbb{R}, \ f(...

Question 9

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(...

Question 10

Let $A=(a_{ik})\in\mathbb{R}^{N\times K}$. Consider the system of equations: $$x_{i}=\sum_{k=1}^{K}a_{ik}\tanh\left( \sum_{j}a_{jk}x_{j} \right)$$ for the vector $\mathbf{x}=(x_{i})\in\mathbb{R}^{N}$, ...

Question 11

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 $(i, j)=(1,3), (2,1), (3,2)$. ...

Question 12

For a system represented by a first order differential equation, which is the most accurate name for it? If I call it a one-dimensional system or 1D system, it can be ambiguous because it can be ...

Question 13

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 ...

Question 14

For differentiable infinitesimals $u_x(x) \in o(x)$ and $u_y(y) \in o(y)$, In the following differential equation: $ \frac{dy}{dt}= x + u_x(x)$ $ \frac{dx}{dt}= -y + u_y(y)$ Is it true that when ...

Question 15

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 ...

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Questions tagged [nonlinear-system]

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