Stability Flashcards
(7 cards)
What is an attractor?
A set of states in state space towards which a system tends to evolve, so that conditions in the basin of attraction will remain close to it, even if disturbed.
Describe two types of attractors.
Two simple types: fixed point attractors and limit cycle attractors.
A fixed-point attractor is a single point in a one-dimensional phase space.
A limit cycle is a periodic orbit on a plane with a closed trajectory, and a limit cycle attractor is a stable limit cycle with a two-dimensional manifold that, because of the closed trajectory, describes periodic behavior.
Describe how to determine stability in a dynamical system and what it means.
Stability can be characterized by different behaviors that occur in the system around an equilibrium point, which can also be thought of as a stationary condition in a system’s dynamics.
An equilibrium point is stable if initial conditions that start nearby remain in the epsilon neighborhood of the point, asymptotically stable if it is both stable and all nearby trajectories direct to it, and unstable if initial conditions diverge away from the equilibrium point.
What is asymptotic stability?
Asymptotic stability in this description can also be known as an attractor. An attractor is considered a set of states in state space towards which a system tends to evolve, so that conditions in the basin of attraction will remain close to it, even if disturbed.
What are damped oscillations?
Any oscillation in which the amplitude of the oscillating quantity decreases with time.
What does a damped oscillation look like in a population?
A population will overshoot and then undershoot the carrying capacity in sequence. The degree to which it undershoots or overshoots, however, will lessen with each timestep, until the population eventually settles on the carrying capacity.
What’s an example of a coupled oscillator in ecology?
Consumer-resource interactions
