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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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Newton method to solve nonlinear system

How can I solve this problem: ${e^x}^y +{x}^2+y-1.2=0 \\ {x}^2 +{y}^2+x-0.55=0$ for various loaded inputs with start points $(x_0 , y_0) = 0.6, 0.5$ Could anybody help me. Thank you in advance
user406304
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Solve non-linear system of four variable

I have the following nonlinear system: \begin{align} 2x-2a-b&=0\\ 2y-a+b&=0\\ a(-2x-2y-1)&=0\\ b(-x+y+4)&=0\\ a, b &\geq 0 \end{align} We can see the solutions here. My question is - how can I solve this system as simply as possible "on paper"?
Eenoku
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domain of attraction for nonlinear system

I have a nonlinear system $x'=Ax+g(x)$ , A is Hurwitz, g is locally Lipschitz and $||g(x)||_2 <= c*||x||_2^2$ , where $||.||_2$ is the 2-norm (Euklid). What is a guess for the domain of attraction? Thank you
Josh
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Gauss-Jordan elimination for systems of power equations

I'm curious as to whether Gauss-Jordan elimination has an equivalent approach for systems of equations involving non-linear terms, for example: $$ \begin{align} x^3 y^3 z^3 &= 1\\ xy^5 z^3 &= 2\\ xy^3 z^5 &= 3 \end{align} $$ I can solve these…
Dmitri Nesteruk
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Replacing variables in a nolinear system by their absolute values

I have to solve a nonlinear system (for some reactions) using newton's method to get molar fractions (positive values), sometimes I get negative values depending on the initial vector, to prevent this, I want to replace variables in the system by…
user265759
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Solving system of equations involving ratios and exponents

I have two equations, $$\frac{x}{1-x}=\exp(A_{x}+Bx+Cy)$$ $$\frac{y}{1-y}=\exp(A_{y}+Cx+Dy)$$ I am interested in the number of solutions $(x,y)$ to these two equations as the parameters $A_{x},A_{y},B,C,D$ vary. If any help, I know that…
John Kim
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Dulac’s negative criteria - in a plane

I am trying to verify that a ODE system, $\dot x=f(x,y), \dot y=g(x,y)$, has no periodic orbits in the plane (presumed to be in $\mathbb R^2$). Thus I need to show for a function $h(x,y)$, that $\dfrac{\partial hf}{\partial x}+\dfrac{\partial…
KidMe
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Non-linear functional form satisfying $g(x-y) = \frac{g(x)}{g(y)}$.

Is there a general non-linear mapping function family, which obeys this general rule: $$g(x-y) = \frac{g(x)}{g(y)}.$$ I am looking at identifying a classification of admissible kinetics relaxation functions.
Babak Safa
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nonlinear system: properties of solutions

I have a nonlinear system of equations which I'm struggling to solve and actually do not have much hope to find an explicit solution. I do not need to solve it; but I want to prove a property of the solution of this system, namely 'monotonicity' of…
Evgeny
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Number of solutions for an underdetermined system of nonlinear equations

Given $n$ independent nonlinear equations in the $n+1$ variables $x_1,\dots,x_{n+1}$, is the solution always of dimension 1? For example, if $n=1$, $x_1\sin(x_1+x_2)=0$ gives a curve in $\mathbb R^2$. It is not clear to me whether this is something…
anderstood
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Plotting x and y according to given equations

Hello i am trying to come up with two resistor values in my school project circuit and i wonder could these two equations give me a x,y plot: $$x*y=20*(x+y) \tag{1} $$ $$x*(y+100)=60*(x+y+100)\tag{2}$$ $$1000>x,y>0 \tag{3}$$ I would be so glad if…
Not a genius
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How to show that a system $dx/dt = f(x,y)$, $dy/dt = f(x,y)$ has a stable limit cycle which lies in the anular region?

I know I need to convert it to polar system but I don't know how to do this My system is $$\dfrac{dx}{dt}= x - y -x(x^2 + 2y^2)$$ and $$\dfrac{dy}{dt} = x + y -y(x^2 + y^2).$$ The annular region is $\frac{2}{\sqrt{5}} < r < 1$, which gives the…
Fred
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A set of nonlinear coupled ODE

I have reached a set of ODE as \begin{align} &\ddot{\vec{a}}(t)+\omega_0^2\frac{\cos{(b(t))}\sin{(a(t))}}{a(t)}\vec{a}(t)=0\\ &\ddot{b}(t)+\omega_0^2\cos{(a(t))}\sin{(b(t))}=0 \end{align} that describes the dynamics of a quantum operator…
Moein Malekakhlagh
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curiousity question on Lyapunov function of a nonlinear system

I've just begun studying nonlinear systems in my spare time. I'm using 'Nonlinear System Theory' by Rugh. My question is if there is a universal way to find the Lyapunov function of an arbitrary system. It doesn't have to be the easiest way, just a…
Desperate Fluffy
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Conditions for existence and uniqueness of systems with linear and nonlinear equations

Given a system that contains a mixture of linear and nonlinear equations, under what conditions can we guarantee that a solution will exist and that it will be unique? For example, the system \begin{align} a^2+b^2&=c^2 && (1) \\ a+b+c&=1000 &&…
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