{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T18:16:44Z","timestamp":1770142604372,"version":"3.49.0"},"reference-count":36,"publisher":"World Scientific Pub Co Pte Ltd","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2024,9,15]]},"abstract":"<jats:p> Discretization schemes such as Euler method and Runge\u2013Kutta techniques are extensively used to find approximate solutions of Continuous-Time (CT) dynamical system. While the approximation is good for small discretization step sizes, as pointed out by Lorenz, when the step size increases, computational chaos and computational instability are frequently observed, the former phenomenon being a precursor to the latter. By computational instability, it is meant that there is a blow up of trajectories for the Discrete-Time (DT) system. Computational chaos instead means that for certain step sizes, the DT system displays chaos while the CT counterpart is not chaotic. This paper studies the dynamics of a class of second-order maps obtained via the discretization of a Memristor Murali\u2013Lakshmanan\u2013Chua Circuit (MMLCC). The discretization, which is based on the DT Flux\u2013Charge Analysis Method (FCAM), guarantees that the first integrals of a CT-MMLCC are preserved exactly for the DT system. Hence the dynamics of DT-MMLCC evolves on invariant manifolds and it is characterized by the coexistence of infinitely many different attractors (extreme multistability). The paper uses analytic techniques introduced by Marotto, based on the concept of snapback repellers and transverse homoclinic orbits, to study the chaotic behaviors of the maps. Regions of the parameter space are singled out where there exist snapback repellers for DT-MMLCC, thus implying that the maps display chaos in the Marotto and in the Li\u2013Yorke sense. Since the corresponding CT-MMLCC does not display chaos, the observed chaos of DT-MMLCC is genuinely a consequence of the discretization scheme used in the paper, i.e. it can be actually considered as computational chaos. It is also verified that computational chaos is a precursor to computational instability of the DT-MMLCC maps. Finally, the paper analyzes the effect on chaos obtained by changing the invariant manifold where the dynamics evolves. <\/jats:p>","DOI":"10.1142\/s0218127424300222","type":"journal-article","created":{"date-parts":[[2024,8,26]],"date-time":"2024-08-26T02:03:05Z","timestamp":1724637785000},"source":"Crossref","is-referenced-by-count":4,"title":["Snapback Repellers, Computational Chaos and Extreme Multistability in Discrete-Time Memristor Murali\u2013Lakshmanan\u2013Chua Circuit"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0013-9112","authenticated-orcid":false,"given":"Mauro","family":"Di Marco","sequence":"first","affiliation":[{"name":"Department of Information Engineering and Mathematics, University of Siena, via Roma 56, 53100 Siena, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3970-7201","authenticated-orcid":false,"given":"Mauro","family":"Forti","sequence":"additional","affiliation":[{"name":"Department of Information Engineering and Mathematics, University of Siena, via Roma 56, 53100 Siena, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2502-9542","authenticated-orcid":false,"given":"Luca","family":"Pancioni","sequence":"additional","affiliation":[{"name":"Department of Information Engineering and Mathematics, University of Siena, via Roma 56, 53100 Siena, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0234-5999","authenticated-orcid":false,"given":"Alberto","family":"Tesi","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, University of Florence, via S. 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