Abstract
In this paper, we detect Unstable Periodic Orbits (UPOs) of both self-excited and hidden attractors using the Damped Newton–Raphson–Mees algorithm. This study answers one of the long-standing questions about the size of a hidden attractor. We observe that the UPOs of the self-excited attractor are spread in a thick region within the phase space at varying distances from the fixed point, whereas the UPOs of hidden attractors are confined to a thin layer. This reveals details concerning the size of a hidden attractor. We demonstrate this for a hidden attractor without a fixed point and for a hidden attractor with a single stable fixed point. To compare the results with self-excited attractors, we have taken Lorenz and Rössler attractor as examples.
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