Abstract
To detect determinism and instability geometrically, the Lorenz map zn+1 = f(zn), which projects a local maximum zn to the next local maximum zn+1 of the time series, is useful for such a thin attractor as the Lorenz attractor, but is not applicable for such a "fat" attractor as the Chua circuit. Hence, this study proposes a novel and simple method that is applicable for various attractors. It shows that a T-delayed Lorenz map zn+T = fT(zn), which projects a local maximum zn to the T-delayed local maximum zn+T, is more useful. It was found that the appearance of a parabolic image in a T-delayed Lorenz map is a sign of chaos.
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