# Questions tagged [non-linear-dynamics]

This tag is for questions relating to nonlinear-dynamics, the branch of mathematical physics that studies systems governed by equations more complex than the linear, $~aX+b~$ form.

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### Propagating in time a Nonlinear Dynamically Inverted (NDI) System

Background Suppose I have a nonlinear system given by $\dot{x}=f(x)+G(x)u$ $y=Hx$ where $x$ is the state, $y$ is the output, $G$ is a control matrix. This form is identical to how one would ...
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### Are there descriptions of nonlinear dynamical systems other than ODEs?

The canonical way to describe a dynamical system is to write it into the state-space representation, i.e., $\dot{x} = f(x, u), y = h(x, u)$. For a linear dynamical system, we can also use the transfer ...
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### finding a closed orbit for an oscillator equation

Consider the oscillator equation $$\displaystyle\ddot{x}+F(x,\dot{x})\dot{x}+x=0$$ where $F(x,\dot{x})<0$ if $r\leq a$ and $F(x,\dot{x})>0$ if $r\geq b$ where $r^2=x^2+\dot{x}^2$. Show ...
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### Is this a correct control input for this nonlinear system

Take a look at this system \begin{align} \dot{x}_1 &= \cos x_2 + (x_2+1)x_3 \tag{1}\\ \dot{x}_2 &= x^3_1+x_3 \tag{2}\\ \dot{x}_3 &= x^2_1+u \tag{3}\\ y&=x_1 \tag{4} \end{align} ...
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### Creating a SIIR (susceptible, infected, isolated, recovered) model using differential equations.

I wasn't too sure of where to post this since it's a mix of physics (dynamical systems), medicine, and mathematics but here it goes. I am trying to model the current outbreak of Covid 19 using a more ...
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### Non-linear ode solution with integral formula

I am trying to figure out how the ode $\dot{x}=x^2, x(0)=c>1$ has the solution $x(t)=(\frac{1}{c}-t)^{-1}$ using the formula $x(t) = x_0+ \int^{t}_{t_0}f(s,x(s))ds$. I tried the substitution ...
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### Two interpretations of Chaos?

Broadly speaking, I cannot pin down what is meant by Chaos. I understand that (informally) if a dynamical system is highly sensitive to initial input data then this system is said to be chaotic. Eg ...