# Attractor

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Related to Periodic attractor: chaotic attractor

## Attractor

In non-linear dynamic series, an attractor defines the equilibrium level of the system. See: Point Attractor, Limit Cycle, and Strange Attractor.
Copyright © 2012, Campbell R. Harvey. All Rights Reserved.
References in periodicals archive ?
The intermittent or periodic attractors of (3) exist for [rho] which lies in the interims (23.6,24].
When the initial values were [[beta].sub.1] ([z.sub.0], [w.sub.0], [[theta].sub.0], [q.sub.0]) = (-0.1924, 0.8886, -0.7648, -1.4023), at the equilibrium point, the system (6) solution converged to a red periodic attractor; when the initial values were [[beta].sub.2] ([z.sub.0], [w.sub.0], [[theta].sub.0], [q.sub.0]) = (-1.0616, 2.3505, -0.6156, -0.7481), the system (6) solution converged to a blue chaotic attractor at the equilibrium point.
(3) Within [sigma] [member of] [0.0262,0.02973], k [member of] [7.387,14.32], the green stable region, the red periodic region, and the divergent region are interwoven; stable equilibrium points coexist with periodic attractors in the region.
The periodic attractor representing the traveling wave can undergo several subsequent bifurcations, such as period doubling bifurcations or Neimark-Sacker bifurcations.
The proposed autonomous jerk oscillator exhibits periodic attractors, one-scroll chaotic attractors,, and coexistence between chaotic and periodic attractors.
It moves from period-1 limit cycle to double band chaotic attractors going through single band chaotic attractors and tiny windows of periodic attractors. Figure 3 (left) illustrates this bifurcation sequence with the numerical phase portraits.

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