basin of attraction

basin of attraction

[′bās·ən əv ə′trak·shən]
(physics)
The collection of all possible initial conditions of a dynamical system for which the trajectories representing that system in phase space will converge to a particular attractor.
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The radius of convergence (Julia set) is an important characteristic of the corresponding basin of attraction. Julia set is the boundary of the area of complex variable values of [X.sub.n], belonging to which ensures the convergence of the iteration expression (2) to the attractor.
If this run converges, algorithm records the start point and the end point for an initial estimate on the radius of a basin of attraction.
Basin of attraction for coexistence of two types of 1-periodic cycles is shown in Figure 10(c); the red region and the dark blue region represent the initial values which make supercavitating vehicle fall into different periods of oscillation eventually.
In nine of these regions the global dynamics is in competitive exclusion case, which means that all solutions converge to one of the equilibrium points on the axes and in only two situations we have competitive coexistence case, which means that the interior equilibrium points have substantial basin of attraction. In all 11 cases, the zero equilibrium has some basin of attraction which is a part of y-axis so we can say that in these cases system (1) exhibits weak Allee's effect.
The more adaptive walks terminating at an optimum, the larger the basin of attraction. In this way the accessibility of a local optimum is a measure of its basin of attraction.
It is known that the basin of attraction of an iterative method on a particular function is an interesting tool to visually get to know how an iteration function behaves as a function of different initial points [19].
Shaikh Mohammed's commitment and care for the Media sector was the direct cause of the success of the UAE in anchoring a thriving and growing industry that constitute of distinguished national institutions that have left their marks on the gulf and Arab media landscapes as well as a number of media free zones that have developed as destinations for Arab and foreign media and a basin of attraction for the largest regional media organisations that have found a healthy environment provided by the UAE.
Basin of attraction of a fixed point ([bar.x], [bar.y]) of a map T, denoted as B(([bar.x],[bar.y])), is defined as the set of all initial points ([x.sub.0], [y.sub.0]) for which the sequence of iterates [T.sup.n](([x.sub.0], [y.sub.0])) converges to ([bar.x], [bar.y]).
In case 3, [E.sub.3] is stable equilibrium, which biologically implies that the two populations will eventually co-exist at [E.sub.3] if the initial size of the two populations is on the basin of attraction of [E.sub.3].
The basin of attraction (referred to hereafter as simply the basin) is the collection of points such that, when the system is initiated at any of them, it winds up at the associated attractor.
In 1992, Alexander and his colleagues found a theoretical example in which the set of initial conditions, or basin of attraction, leading to one attractor is riddled with points corresponding to initial conditions leading to another outcome.