{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T06:01:56Z","timestamp":1768802516607,"version":"3.49.0"},"reference-count":29,"publisher":"World Scientific Pub Co Pte Ltd","issue":"13","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2023,10]]},"abstract":"<jats:p>In this paper, spikes adding to infinity on bifurcation trees of period-1 orbits to chaos in the R\u00f6ssler system is studied. The spikes adding on the periodic orbits is completed through a saddle-node bifurcation. With onset of a period-1 orbit, there is 1-spike on such a period-1 orbit, followed by the development from 1-spike to [Formula: see text]-spikes and the period-1 to period-[Formula: see text] orbits have 1-spike to [Formula: see text]-spikes. For a spike bifurcation of a period-1 orbit with [Formula: see text]-spikes ([Formula: see text]), a new spike is added on such a period-1 orbit. Thus, the period-1 orbit has [Formula: see text]-spikes. Such a period-1 to period-[Formula: see text] orbits ([Formula: see text]) have [Formula: see text]-spikes to [Formula: see text]-spikes. The three bifurcation trees of period-1 orbits with [Formula: see text]-spikes ([Formula: see text]) to period-4 orbits with [Formula: see text]-spikes are presented numerically. The phase trajectories and responses of [Formula: see text]-component for period-1 to period-4 orbits with different spikes are given for illustrations of spikes adding on periodic orbits. The spikes adding generating the complexity of period-1 orbits to chaos can be developed.<\/jats:p>","DOI":"10.1142\/s0218127423300331","type":"journal-article","created":{"date-parts":[[2023,10,31]],"date-time":"2023-10-31T02:10:07Z","timestamp":1698718207000},"source":"Crossref","is-referenced-by-count":5,"title":["Spikes Adding to Infinity on Period-1 Orbits to Chaos in the R\u00f6ssler System"],"prefix":"10.1142","volume":"33","author":[{"given":"Siyuan","family":"Xing","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, California Polytechnic State University, San Luis Obispo, CA 93407, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8208-6108","authenticated-orcid":false,"given":"Albert C. 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