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| Complex Wada Basin Analysis of Infinite Coexisting Attractors in a Class of Oscillators |
| WANG Jingwei
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| School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China |
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Abstract 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 attractors that share common basin boundaries, and these attractors exhibit periodic spatial distributions. 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 essential 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 conditions.
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Received: 10 May 2023
Published: 03 January 2025
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