# 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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### Solving for constant of a known nonlinear dynamic system, numerically

Given a dynamic system, \begin{equation*} \frac{d\vec{s}}{dt}=f(t,\vec{s},\vec{c}) \end{equation*} where $\vec{s}$ are the state, and $\vec{c}$ are constants. And $\vec{s_0},\vec{s_1},...\vec{s_n}$ ...
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### Zero set of system of two real quadratic forms

Background: Consider the equation $x^T A_1 x = 0$ where $x \in \mathbb{R}^\mu$ and $A_1 \in \mathbb{R}^{\mu \times \mu}$ is a symmetric matrix. Suppose we also demand the normalization $x^T x = 1$. ...
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### Algorithm for non-linear system of equations

I would like some tips in figuring out a good algorithm to find the solution of the following system. Let $\theta$ be a constant in $(0,1)$, let $i,l=1,...,N$, let $a_{l}$ and $b_{i,l}$ be some ...
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### Prove iterations of quadratic maps tends to $-\infty$

So far, I have to read about quadratic map in "Introduction to Dynamical Systems" by Brin and Stuck. The quadratic map is $$q_{\mu}(x) = \mu x(1-x), \quad \mu > 0.$$ Now, I need to show ...
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### How large the error ball of $\|x\|$is, when using the Lyapunov function $x^\top Px$?

I would like to know how large the error ball of $\|x\|$ is when using the Lyapunov function $x^\top Px$: Assumption: I have an almost linear closed-loop system $\dot{x}=(A-BK)x+\epsilon(x)$ with ...