Nonlinear systems Definition and 19 Threads

I developed a program to solve the nonlinear system below through the method of successive approximations and was only able to find one solution, namely ##x_1 = 0.93377## and ##x_2 =0.88417##, even though I tried many different starting points. I was wondering if there's a way to determine if...

I would like to solve this system, which is a sets of non linear quadratic equations, the system needed to be solved can be expressed in general as follow: ϒϒ'C – ϒα = B Where ϒ=(ϒ1,ϒ2,...ϒn)’ is a column vector and ϒ’ its transpose C=(c1,c2,…,cn)’ and B=(b1,b2,…bn)’ are a columns vector And...

Homework Statement Consider the Kortweg-de Vires Equation in the form $$\frac{\partial \psi}{\partial t}+\frac{\partial^3 \psi}{\partial x^3}+6\psi\frac{\partial \psi}{\partial x}=0$$ Find the relation between the coefficients ##c## and ##d## , such that the following quantity is conserved...

So I'm reading the Example on page 161 of Differential Equations, Dynamical Systems and an Introduction to Chaos by Hirsh, Smale, and Devaney. I'm not understanding everything. So given the system x' = x + y^2 y' = -y we see this is non-linear. I get it that near the origin, y^2 tends to...

Homework Statement Given the equation \ddot{\theta}=\Omega^2\sin{\theta}\cos{\theta}-\frac{g}{R}\sin{\theta} Determine a first-order uniform expansion for small but finite theta. Homework Equations Other than the equation above, none so far as I am aware. The Attempt at a...

Hi everyone, I've got an optimisation/computing question. I have a system of nonlinear equalities and inequalities, which I've written below for reference. It's the conditions for a minimiser of a Karush-Kuhn-Tucker problem. Would anyone be kind enough to explain how I could use software to...

Hello, my question is that almost all textbooks say that a linear system will give the output to a weighted sum of impulses which equals the superposition of scaled responses to each of the shifted impulses. But if we apply the same input which is a weighted sum of impulses to a non linear time...

Lately I have been reading about nonlinear systems and chaos. It's fascinating and I would like to know more about how I could prepare myself to possibly study this in grad school. I would be interested in looking at biological systems such as neural networks or even animal populations. I'm a...

Like linear algebra goes in depth about linear systems, what should I look for to learn about the extension of linear algebra to nonlinear systems? Is there a name of the field of study? If I go into a book store to buy books about it, what should I be looking for? Abstract Algebra? Complex...

Ok, to start off I have been examining the structure of polynomials. For instance, consider the general polynomial P(x)=\sum^{n}_{k=0}a_{k}x^{k} (1) Given some polynomial, the coefficients are known. Without the loss of generality...

if we are given a polynomial s^6+as^5+bs^4+cs^3+ds^2+es+k (if a,b,c,d are known) what is a clever method to solving for the value k if we are given the following: the above polynomial is equal to the following(zeta is given as some constant, say 1 for simplicity)...

As the thread title says I'm interested in Chaos Theory, Complex Systems, and Nonlinear Systems. If I can help it, I'd like to study these at graduate level. My question is what kind and how much mathematics I'm supposed to know if I'm to study these?

The complete question I've been given: The Rossler equations are formally defined as dx/dt=−y−z dy/dt=x+ay dz/dt=b+z(x−c). Let us suppose that a=0.2, b=0.2, c=5.7, x(0)=y(0)=z(0)=0, t∈[0,400]. Let v1(t) be the solution to the given initial value problem, and let v2(t) be the solution of the...

Hi, So I keep making mistakes trying to find all of the equilibrium points of different simple nonlinear systems. These problems aren't difficult, it's just that I keep taking different approaches to finding the equilibrium points. Is there a methodological way to know that I have found...

Homework Statement solve the system of 3x^{2}+2y^{2}=35 and 4x^{2}-3y^{2}=24 Homework Equations The Attempt at a Solution I re arranged for y^2 and got 1\frac{1}{3}x^{2}-16=y^{2} I keep getting x to equal \pm 2.473 this is clearly wrong, the answers...

Homework Statement Solve the nonlinear system. x^2-2y^2=16 x^2+y^2=25 Homework Equations n/a? The Attempt at a Solution ive tried subtracting 1 equation from the other... (x^2-2y^2+9)=25 -(x^2+y^2)=25 -3y^2+9=25 -3y^2=16 y^2=-16/3 y=root of -16/3... im not even sure...

Hello, What happens when phasor analysis is applied to nonlinear systems? could someone explain me how it would work? :confused: Thanks

so I'm doing these lagrangian multipliers in calc class and it involves nonlinear systems and apparently the techniques I'm used to applying to linear systems aren't appropriate because i keep losing solutions, getting the wrong ones etc. so yea what are some efficient algorithms for this

Ive been working on a bunch of non linear systems problems for homework and can't figure this one out: y=xcubed x-y=0 I get to the substitution stage and get x-xcubed=0, but you can't factor that so I am wondering what you do next to get the answers for x, and y. Thanks in advance for...