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In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Maps may be parameterized by a discrete-time or a continuous-time parameter.
Confusion matrix is not limited to binary classification and can be used in multi-class classifiers as well. The confusion matrices discussed above have only two conditions: positive and negative. For example, the table below summarizes communication of a whistled language between two speakers, with zero values omitted for clarity. [20]
Both the logistic map and the sine map are one-dimensional maps that map the interval [0, 1] to [0, 1] and satisfy the following property, called unimodal . = =. The map is differentiable and there exists a unique critical point c in [0, 1] such that ′ =. In general, if a one-dimensional map with one parameter and one variable is unimodal and ...
A classification model (classifier or diagnosis [7]) is a mapping of instances between certain classes/groups.Because the classifier or diagnosis result can be an arbitrary real value (continuous output), the classifier boundary between classes must be determined by a threshold value (for instance, to determine whether a person has hypertension based on a blood pressure measure).
The Duffing map (also called as 'Holmes map') is a discrete-time dynamical system. It is an example of a dynamical system that exhibits chaotic behavior . The Duffing map takes a point ( x n , y n ) in the plane and maps it to a new point given by
the identity map id X : (X, τ 2) → (X, τ 1) is a continuous map. the identity map id X : (X, τ 1) → (X, τ 2) is a strongly/relatively open map. (The identity map id X is surjective and therefore it is strongly open if and only if it is relatively open.) Two immediate corollaries of the above equivalent statements are
Maps of certain kinds have been given specific names. These include homomorphisms in algebra, isometries in geometry, operators in analysis and representations in group theory. [2] In the theory of dynamical systems, a map denotes an evolution function used to create discrete dynamical systems. A partial map is a partial function.
In continuous systems, this corresponds to the real part of an eigenvalue of an equilibrium passing through zero. In discrete systems (described by maps), this corresponds to a fixed point having a Floquet multiplier with modulus equal to one. In both cases, the equilibrium is non-hyperbolic at the bifurcation point. The topological changes in ...