# All Questions

8 questions
Filter by
Sorted by
Tagged with
1answer
45 views

### Poincaré Map (Quasi-periodicity; Stability)

In a Poincaré map, when quasi-periodicity is exhibited by the dynamical system, what does it mean in terms of stability for the dynamical system?. Why is it so that as Maximum Lyapunov exponent (MLE) ...
1answer
54 views

### Defining a 'small disturbance which dampens in time' while identifying stable points in a nonlinear system

I'm reading the book "Nonlinear dynamics and Chaos" by S Strogatz. In section 2.2, titled "Fixed points and stability", he defines equilibrium points as solutions where ...all sufficiently small ...
1answer
91 views

### Classification of fixed points in 4D phase space

The usual classification of fixed points as used in linear stability analysis is based on planar systems (un-/stable node, un-/stable spiral point, saddle). I need to extend this classification to a ...
1answer
91 views

### Finding the stability from the eigenvalues of two second-order DEs

I'm analysing the stability of a double physical pendulum, and have determined the dimensionless system of equations to be \begin{align} \label{eq:dimensionless} \begin{aligned} & \ddot{\...
0answers
183 views

### Nonlinear stability question

I am looking for a simple example where a system is linearly unstable, but nonlinearly unstable or stable, depending on the sign of the initial perturbation. For instance, assume the linear normal ...
2answers
87 views

### Question about a Attractors in Non-linear Systems

I've recently been reading up on non-linear dynamics and came across the concept of attractors. I'd like to ask if the concept of attractors can be used for pedestrian egress from a room? Since ...
3answers
787 views

### How to do linear stability analysis on this system of ODEs?

I was trying to do linear stability analysis of spring pendulum. I arrived at the differential equations which describe the system. But I am unable to proceed to linear stability analysis. Is it ...
1answer
135 views

### Stability theory [closed]

I'm studying stability theory recently and met a lot of phrases like linear stability and nonlinear instability. After searching on Google, I became more confused. Thus I wonder if there is any ...