# Questions tagged [nonlinear-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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### Does a spiral fixed point going from stable to unstable always indicate Hopf bifurcation?

Does a spiral fixed point going from stable to unstable (with change in some parameter) always indicate Hopf bifurcation? Could it be a homoclinic bifurcation instead? (Homoclinic bifurcation keeps ...
• 665
1 vote
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### Pontryagin Maximum Principle with terminal and initial conditions

Consider a control problem with Lagragian $L(t,x,u)$ (where $u$ is the control, $x \in \mathbb{R}^d$ the state) and dynamics $\dot{x}=f(x,u,t)$. I have mostly seen problems in which the dynamical ...
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1 vote
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### Show the system has one equilibrium point

I was wondering how we would show that the system: dx/dt=-x^3+2x-4y dy/dt=-y^3+2y+4x has only one equilibrium point. I have seen cases where the system is, ...
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1 vote
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### Solving steady state diffusion with non-linear decay

I want to solve steady state diffusion with constant production term (in the source $[-L_s, 0]$) and a non-linear degradation term, where degradation takes place over the whole domain $[-L_s, L]$, but ...
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### How to find the correct upper and lower bound of a matrix

I am trying to find a correct upper and lower bound for an equilibrium point of the dynamics of matrix R. The equilibrium point is given as: $$R = ARA' + C$$ and I have been able to solve this ...
• 21
1 vote
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### How to render soliton solutions of nonlinear Schrödinger equation exponentially unstable?

The nonlinear Schrödinger equation in $\mathbb{R}^{3+1}$ is $$\phi_t + \nabla^2 \phi + f(|\phi|^2)\phi + V(x)\phi= 0, \quad \phi(x,0) = \phi_0(x).$$ (I require $\phi$ to be square-integrable, and also ...
1 vote
19 views

### nonlinear differential equation for the hypocycloid

I've been trying to tackle a nonlinear first order differential equation that appears when trying to solve the brachistochrone problem through earth's gravitational field. Although being a long and ...
1 vote
36 views

### How Achieve This Specific Non-Linear Mapping

Let's say in a computer program, we have a Slider whereby a user selects a value. The slider widget itself produces a value, X, from 0.0 to 1.0. This value then maps to some other range. Most people ...
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