Complex Wada Basin Analysis of Infinite Coexisting Attractors in a Class of Oscillators
To explore the question of whether there exist common Wada basin boundaries among an infinite number of coexisting attractors,we extended Nusse-Yorke's theorem for finite Wada basins to the scenario of infinite Wada basins.Through numerical experiments conducted on a class of nonlinear oscillators,we discovered that within this class,there are infinite coexisting at-tractors that share common basin boundaries,and these attractors exhibit periodic spatial distri-butions.Further analysis of the intricate Wada basin structures associated with these attractors,employing a generalized version of Nusse-Yorke's theorem concerning Wada basins,confirmed the presence of common boundaries among these interconnected Wada basins.Finally,it is essen-tial to note that this type of Wada basin boundary exhibits highly complex nonlinear dynamical characteristics,potentially leading to significant uncertainty and extreme sensitivity to initial con-ditions.
wada basinbasin of attractioncoexisting attractorsmegastability
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