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The nonlinear three-dimensional map X^. = -(Y+Z) (1) Y^. = X+aY (2) Z^. = b+XZ-cZ (3) whose strange attractor is show above for a=0.2, b=0.2, and c=8.0.

An attractor is a set of states (points in the phase space), invariant under the dynamics, towards which neighboring states in a given basin of attraction asymptotically ...

The Lorenz attractor is an attractor that arises in a simplified system of equations describing the two-dimensional flow of fluid of uniform depth H, with an imposed ...

An attracting set that has zero measure in the embedding phase space and has fractal dimension. Trajectories within a strange attractor appear to skip around randomly. A ...

There are at least two maps known as the Hénon map. The first is the two-dimensional dissipative quadratic map given by the coupled equations x_(n+1) = 1-alphax_n^2+y_n (1) ...

A stable fixed point of a map which, in a dissipative dynamical system, is an attractor.

The set of points in the space of system variables such that initial conditions chosen in this set dynamically evolve to a particular attractor.

A two-dimensional map similar to the Hénon map but with the term -alphax_n^2 replaced by -alpha|x_n|. It is given by the equations x_(n+1) = 1-alpha|x_n|+y_n (1) y_(n+1) = ...

Consider a set of points X_i on an attractor, then the correlation integral is C(l)=lim_(N->infty)1/(N^2)f, where f is the number of pairs (i,j) whose distance |X_i-X_j|<l. ...

Let R(z) be a rational function R(z)=(P(z))/(Q(z)), (1) where z in C^*, C^* is the Riemann sphere C union {infty}, and P and Q are polynomials without common divisors. The ...