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Fractal–Fractional Modeling of Chaotic Inputs in Neuronal Systems: The Rössler–FitzHugh–Nagumo Framework | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 12 آبان 1405 اصل مقاله (2.82 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.70257.3478 | ||
| نویسندگان | ||
| Mahesh Nagpurkar؛ Krunal B Kachhia* | ||
| Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences, Charotar University of Science and Technology, Changa, Anand--388421, Gujarat, India. | ||
| چکیده | ||
| This study examines a fractal–fractional Rössler system and its role as a chaotic input to the FitzHugh– Nagumo (FHN) neuron model. The introduction of fractional order μ and fractal dimension ν allows the incorporation of memory effects and structural heterogeneity. Numerical results show that the Rössler system follows a period–doubling route to chaos, where increasing μ suppresses oscillations and delays chaos, while decreasing ν enhances irregular dynamics. When coupled to the FHN neuron, the chaotic input induces transitions from regular spiking to chaotic firing. All simulations are performed using a predictor–corrector numerical scheme, which demonstrates stable and accurate performance for fractal–fractional systems. These results highlight the effectiveness of fractal–fractional modeling in capturing realistic neuronal and chaotic dynamics. | ||
| کلیدواژه‌ها | ||
| Fractal–fractional calculus؛ Rössler chaotic system؛ FitzHugh–Nagumo neuron model؛ Bifurcation and stability analysis؛ Chaotic neuronal dynamics | ||
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آمار تعداد مشاهده مقاله: 4 تعداد دریافت فایل اصل مقاله: 5 |
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