Summary
A four-variable ordinary differential equation with hyperchaos is investigated further numerically. A self-similar Sierpinski-type fractal is found in a plane of initial conditions if the prospective fate of each point (whether it escapes through the one or the other escape hole in the exploded hyperchaotic attractor) is used for a coloring criterion. A basin boundary of the same qualitative shape therefore exists in either this equation or a closely related one. All hyper-chaotic systems are eligible for an analogous investigation — both numerically and, if possible, experimentally.
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Rossler, O.E., Hudson, J.L., Klein, M., Mira, C. (1990). Self-Similar Basin Boundary in a Continuous System. In: Schiehlen, W. (eds) Nonlinear Dynamics in Engineering Systems. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83578-0_33
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DOI: https://doi.org/10.1007/978-3-642-83578-0_33
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