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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.

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. Reference: Wikipedia.

In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the unknown variables or functions that appear in it (them).

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Linearization of nonlinear state equation around working points

I'm confused about equilibrium points and operating points, are they two different things or the same thing? How would one (or what are the steps to) solve the following equation if operating points are given: $x_{10}=1$ ,…
Pinco Pallino
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Problem with system of nonlinear equations

I need help for one math project. It's about a system of non-inear equations. The system go like this: $$ f(x)=\left\{ \begin{array}{ll} x^5+y^3*z^4+1 \\ x^2*y*z \\ z^4-1 \end{array} \right. $$ The right side of the equation is 0. a) Calculate…
Bambus
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In Nonlinear dynamics, specially refering to strogatz book) what does he mean by $\dot{x}$?

What is the difference between $\dot x$ and f(x), I mean he uses the two interchangeably, especially in example 2.5.1 on page 27. I know that $\dot x$ means the derivative of x with respect to time; $\frac{dx}{dt}$, but is the x a function of t?…
jaghori
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Any theorem on the existence and uniqueness of a system of nonlinear equations?

I'm now solving a system of nonlinear equations (not differential equations). Although I'm able to find a solution for some parameter sets, there are also cases when I can't find a solution. So I'm quite curious about the existence and uniqueness of…
Pu Zhang
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Solve system of non linear equations

I am trying to solve the following system of non linear…
JFNJr
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How should I approach solving non-linear equations?

I need help creating a method for a program I'm making. I've worked on this countless hours and I can not seem to figure it out. what I need: A method that returns $x$. My variables ( initialized to a given number ): double initial, initial2,…
Basam
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analytic solution of system of non-linear algebraic equations

Can we solve analytically a system of non-linear algebraic equations? In particular something of this form( $x_k$ are the unknowns): $$b_1 = a_{11}x_1 + a_{12}x_2+....+ a_{1k}x_k$$ $$b_2 = a_{21}x_1^2 + a_{22}x_2^2 + .....+ a_{2k}x_k^2$$ $$b_3 =…
user304876
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Dynamically non-linear increment

I have a range of percentage like 10% to 80%. Now, I want to divide this range non-linearly in 6 parts so the 2nd part will be greater than 1st. So minimum value is 10% and it will scale up to 80% and the increase will be greater each time. Please…
Girish
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Bendixson's condition for existence of limit cycle for a nonlinear system

I encountered this example in Slotine,Lee:Nonlinear Control book. Consider the nonlinear system $$\dot{x_1} = g(x_2) + 4x_1x_2^2$$ $$\dot{x_2} = h(x_1) + 4x_1^2x_2$$ Is there a limit cycle on phase plane? The solution calculates…
Zeta.Investigator
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Equilibrium Points and Linearization

Consider the planar nonlinear system, $x' = a − x − \frac{4xy}{1 + x^2}$ $y' = bx(1− \frac{ y}{1 + x^2})$ where $x$ and $y$ represent the concentrations of $I-$ (iodine ions) and $ClO_2-$ (chlorine dioxide ions), respectively, and $a$ and $b$ are…
Li Xun
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Nonlinear system, how to find Lyapunov

The nonlinear system: $\dot{x}_1 = \frac{5}{2}-2x_2-\frac{3}{2}x_1+x_2x_1$ and $\dot{x}_2 = x_1-1$. How do I find the Lyapunov function of this system? Or how to determine the existence of such a function? I know there's an equilibrium point at…
Desperate Fluffy
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Finding the Lyapunov of the system

The nonlinear system is: $\dot{x}_1=\frac{5}{2}-2x_2-\frac{3}{2}x_1+x_2x_1$ and $\dot{x}_2=x_1-\frac{5}{2}$. My problem is trying to find the Lyapunov function for this system, if one exists. I've been using the Sums of Squares Method, but it…
Desperate Fluffy
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Finding solution of nonlinear differential system

$$x'=2x+y^2$$ $$y'=y$$ How to find a solution of above system if $x>0$? I found a solution of second equation, $y=y_0e^t$, but don't know how to use this to solve the system. Thanks.
rekt
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Formula question (non-linear?) Y and X

I am trying to come up with a formula so I can get the value of $X$, with whatever $Y$ I put in. A few example values are listed down below \begin{matrix} Y & X \\ 1 & 0.9 \\ 10 & 0.5 \\ 100 & 0.3 \\ 1000 & 0.2 \\ 10000 & 0.15 \\ 100000 &…
Nick van Wersch
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funny money exchange

Say a friend agrees to square my pocket change, I have 10 x 10p coins = £1. He gives me 100 x 10p coins, I have £10 Next day I have 100 x 1p coins also = £1, he gives me 100 x 100 x 1p = £100 Why ?
xatabay
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