{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T19:52:06Z","timestamp":1770839526546,"version":"3.50.1"},"reference-count":29,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,11,12]],"date-time":"2021-11-12T00:00:00Z","timestamp":1636675200000},"content-version":"vor","delay-in-days":315,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>It is important to investigate the firing activities of neurons, and previous experimental works have shown that fractional\u2010order neuronal models depict the firing rate of neurons more verifiably. In this study, a modified fractional\u2010order Hindmarsh\u2013Rose neuronal model is proposed, and the dynamics and firing activities are investigated. Some novel phenomenon can be found. First, by analyzing numerically and theoretically, the Hopf bifurcation is found to occur when the external direct current stimulus is chosen appropriately. The effects of fractional\u2010order on the bifurcation are also studied. Second, when injecting a direct current stimulus, compared with the integer\u2010order model, the system has more varying dynamic behaviors and firing pattern transitions. Under different external current stimulus, periodic firing patterns and chaotic firing patterns occur when fractional\u2010order changes, but the regions of chaotic firing patterns are different. In other words, the transition mode of periodic firing and chaotic firing induced by fractional\u2010order is different under different external current stimulus. The two\u2010dimensional colored diagram of firing patterns is also investigated. Finally, when injecting periodic current stimulus, regular\/irregular bursting, multiple spiking, regular\\irregular square wave bursting, and mixed firing mods are found by setting the appropriate fractional\u2010order, amplitude, and frequency of the external current stimulus. Some firing patterns cannot be found in integer\u2010order models. When the amplitude is chosen at appropriate values, the region of frequency when the system displays the mixed firing modes decreases with increasing fractional\u2010order.<\/jats:p>","DOI":"10.1155\/2021\/8490695","type":"journal-article","created":{"date-parts":[[2021,11,13]],"date-time":"2021-11-13T03:20:05Z","timestamp":1636773605000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Diverse Dynamic Behaviors and Firing Activities of the Modified Fractional\u2010Order Hindmarsh\u2013Rose Neuronal Model Induced by 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