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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2025,8]]},"abstract":"<jats:p> This paper focuses on a discrete memristor-coupled bi-Rulkov neuron model. Regarding the model construction, a discrete flux-controlled memristor is used to couple two Rulkov neurons, thereby simulating the electromagnetic induction effect between the coupled neurons. This model possesses a line fixed-point set which depends on the initial value of the memristor, and its stability is analyzed. The dynamical behaviors are explored through bifurcation diagrams, Lyapunov exponents, iterative diagrams, phase diagrams, spectral entropy, and [Formula: see text] complexity. The diverse results including chaos, hyperchaos, initial-value-dependent bifurcation routes, and coexisting attractors are revealed. Subsequently, the dynamic effects resulting from the initial condition of the memristor are examined, and diverse firing patterns relying on the memristor parameters are clarified. Meanwhile, the memristor initial-boosted behavior is theoretically analyzed, and it is found that the model displays extreme multistability behavior boosted by the memristor initial states. In particular, infinitely many coexisting homogeneous hyperchaotic attractors are discovered, which are boosted by the initial value of the memristor nondestructively. They exhibit relatively high complexity and have potential applications in encryption. The initial-value-related heterogeneous multistability is investigated. Finally, analog circuits of the memristor and coupled system are designed theoretically. <\/jats:p>","DOI":"10.1142\/s0218127425501251","type":"journal-article","created":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T06:05:49Z","timestamp":1751004349000},"source":"Crossref","is-referenced-by-count":2,"title":["Hyperchaos and Extreme Multistability in a Discrete Memristor-Coupled Bi-Rulkov Neuron Model"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-3370-1308","authenticated-orcid":false,"given":"Xiuquan","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Qufu Normal University, Qufu 273165, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5250-6957","authenticated-orcid":false,"given":"Ming","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Qufu Normal University, Qufu 273165, P. R. 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