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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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System of non linear equations, find a good initial guess

I don't know if this is the right section to ask this question. I have to find the solutions of: \begin{align} & k_r^*=\sum_{c=1}^{N_C} \frac{x_ry_c}{1+x_ry_c} \ \ \ r=1,...,N_R\\&h_c^*=\sum_{r=1}^{N_R} \frac{x_ry_c}{1+x_ry_c} \ \ \…
Peanojr
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Need help understanding algebra move made to solve system of two non-linear equations

I need help understanding the following: Two equations are derived, each from a different set of constraints that don't enforce each other. That is, the $x, y$ relationship in equation (1) is not the same as the $x, y$ relationship in equation (2).…
Malcolm Regan
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Need help solving a system of nonlinear equations - SIRS model

I am working on a research paper and developing a modified SIRS model with the following equations. S˙ = −αS − β(1 − ξ)SA − βξSP + εP + δR + µ(P + R) + µ*A P˙ = αS − (ε + γ + µ)P A˙ = γP + σR + β(1 − ξ)SA + βξSP + νRA − (ζ + µ*)A R˙ = ζA − νRA −…
CashCab1221
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Two nonlinear equations (quadratic) in two unknowns

I would like to solve the following system of equations: $$ \left\{ \begin{array}{r} a x^2 + b x y + c_1 x + c_2 y + d_1 = 0 ,\\ a y^2 + bxy + c_3 x + c_4 y + d_2 = 0 . \end{array} \right. $$ Here, $a,b,c_i , d_i$ are known constants and I want to…
PattiMusic
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Solution of System of Bivariate Cubic Polynomials

Apart from numerical solutions, is there a method to find the real roots of $X$ and $Y$ for this system of nonlinear equations ? $X^3 -3 X Y^2 + b_1 X - b_2 Y + c_1=0$ $Y^3 -3 X^2 Y - b_1 Y - b_2 X - c_2=0$ where $b_i$ and $c_i$ are real…
Paulo J. P. Gonçalves
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Neural network as a nonlinear system?

I defined a very simple neural network of $2$ inputs, $1$ hidden layer with $2$ nodes, and one output node. For each input pattern $x⃗ ∈ ℝ×ℝ$ and associated output $o∈ℝ$, the resulting nonlinear equation is: $wo_{0} σ(x_0 Wi_{00} + x_1 Wi_{10}) +…
Filippo Portera
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Equilibrium points for nonlinear system with constant input

I'm trying to find the equilibrium points of a nonlinear model where input u=u* <1 is constant. T and $\zeta$ are given. $\dot{x}_1 = x_2\qquad\qquad\qquad\qquad\qquad$ (1) $\dot{x}_2 = -x_1-2\zeta x_2+\frac{1}{3}x_3^2\qquad\qquad$ …
user613221
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Fixed points and Stability (Nonlinear System)

$$\dot x = -x + x^3$$ $$\dot y = x + y$$ Where $(x,y) \in \mathbb{R^2}$ I found the fixed points to be: $$(0,0),(0,1),(0,-1),(1,0),(1,1),(1,-1),(-1,0),(-1,1),(-1,-1)$$ The Jacobian Matrix to be: \begin{bmatrix} -1+3x^2 & 0\\ 1 …
Jon
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System of non-lineair equations

I can't find the solutions of this system of equations. I only need the "whole number" solutions. The solutions I'm searching for: $x=-1 \land y = 1 \land \lambda = \frac{1}{2e}$ \begin{cases} \begin{array} {rcl} e^{x+y-y^2}+2\lambda x \ = 0 \\…
ndswaef
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Given positive parameters $a,b$ how can one tell when a Hopf Bifurcation occurs?

Consider the system $\frac{dx}{dt}$=$2-(b+1)x+ax^{2}y$ $\frac{dy}{dt}$=$bx-ax^{2}y$ For what values of a and b does a Hopf Bifurcation occure, given that a and b are positive, and in the region x,y ≥0 I found that the system had only one fixed point…
Robbie Meaney
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Under what conditions is this system uniquely satisfied?

I have a system of two nonlinear equations: $$\theta_{LB}=\frac{1}{k_{LB}} \left[\frac{k_{LG}}{(1-\delta_L)\Delta q(\theta_{LG})} -(1-\beta_L)(y_{LG}-z_L)-(1-\beta_L)k_{LG}\theta_{LG} \right]$$ $$\theta_{LG}=\frac{1}{k_{LG}} \left[…
user432299
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How to write the following equation in dimensionless form?

We have the following equation $$mg\sin(\theta)=kx\left(1-\frac{L}{\sqrt{x^2+a^2}}\right)$$ and we are asked to put it in the following dimensionless form: $$1-\frac{h}{u}=\frac{R}{\sqrt{1+u^2}}.$$ According to me $u=x/a$ and $R=L/a$ then we have…
Student
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backstepping control of third order non linear system.

I have the following question from an exercise set of the course "Control of Non Linear Mechanical Systems." It involves so called integrator backstepping. And I've got a vague idea from a website how it must be done but I'm looking for a simple…
user463102
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Nonlinear system: need some advice.

I need to solve this nonlinear system of equations. Coefficients a,b,c,d are given. Since it is a system of 4 eq. and 4 unknowns $x_{i}$ it should have a solution but unfortunately there are the squares... Is there any way to solve this in…
Mark
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Most widely used software for complex-system researchers

Now I started to learn the basics regarding analysis of complex systems theory. I am especially concerning about studying non-linear dynamic systems and trying to simulate some examples denoted on my textbook. I had several options - such as…
Daschin
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