乐胖代购免代理版

{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,10]],"date-time":"2025-04-10T08:34:56Z","timestamp":1744274096571,"version":"3.37.3"},"reference-count":62,"publisher":"World Scientific Pub Co Pte Ltd","issue":"16","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12272230"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2023,12,30]]},"abstract":" A liquid bath vibrating vertically can lead to the emergence of a self-propelled walking droplet on its free surface, which can exhibit chaotic motion. It is well-known that trajectories of a chaotic system are sensitive to its initial condition, known as the \u201cbutterfly-effect\u201d, while its statistics normally remain stable to small disturbances: this type of chaos is called \u201cnormal-chaos\u201d. However, a concept called \u201cultra-chaos\u201d has been recently introduced, whose statistical features are unstable, i.e. extremely sensitive to small disturbances. Up to now, a few examples of ultra-chaos have been reported. In this paper, the influence of tiny disturbances on the motion of walking droplet is investigated. It is found that both normal-chaos and ultra-chaos exist in the motion of the walking droplet. Different from the normal-chaotic motion, even the statistical properties of the droplet\u2019s ultra-chaotic motion are sensitive to tiny disturbances. Therefore, this illustrates once again that ultra-chaos indeed exists widely and represents a higher disorder compared with normal-chaos. The ultra-chaos as a new concept can widen our knowledge about chaos and provide us with a new point of view to study chaotic properties. It should be emphasized that, for an ultra-chaos, it is impossible to repeat any results of its physical experiments or numerical simulations even in the meaning of statistics! Unfortunately, reproducibility is a corner stone of modern science. Thus, the paradigm of modern scientific research might be invalid for an ultra-chaotic system. <\/jats:p>","DOI":"10.1142\/s0218127423501912","type":"journal-article","created":{"date-parts":[[2023,12,30]],"date-time":"2023-12-30T06:56:24Z","timestamp":1703919384000},"source":"Crossref","is-referenced-by-count":2,"title":["Ultra-Chaos in the Motion of Walking Droplet"],"prefix":"10.1142","volume":"33","author":[{"given":"Yu","family":"Yang","sequence":"first","affiliation":[{"name":"School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, P. R. China"}]},{"given":"Shijie","family":"Qin","sequence":"additional","affiliation":[{"name":"School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2372-9502","authenticated-orcid":false,"given":"Shijun","family":"Liao","sequence":"additional","affiliation":[{"name":"School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, P. R. China"},{"name":"State Key Laboratory of Ocean Engineering, Shanghai 200240, P. R. 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