发表机构
University of Ferrara（费拉拉大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究Rulkov神经映射的交叉耦合，通过分析证明其能保持运动有界性等，对两个标准混沌Rulkov映射耦合进行数值模拟，展示全局奇异吸引子等，还进行多项数值研究，并简要提出耦合到任意数量神经元的推广方法。
AI 中文摘要
我们引入了一种新型的Rulkov神经映射耦合，为作用于慢变量的微扰向非小值转变提出了一种启发式生物学解释。我们通过分析证明，如果耦合与原始系统相关联，它能保持运动的有界性和骤回排斥子的存在性（根据Marotto定理导致Devaney混沌）。对于两个标准混沌Rulkov映射的耦合，我们给出了系统轨道的数值模拟，显示出全局奇异吸引子的出现，其分形结构通过非整数Kaplan - Yorke维数的计算得到有力暗示。此外，我们还进行了关于时间序列、Lyapunov指数谱、分岔图和吸引盆的标准数值研究。最后，我们简要提出了将耦合推广到任意数量神经元的方法。
英文摘要
We introduce a novel coupling of Rulkov neural maps, proposing a heuristic biological interpretation for the transition to non-small values of the perturbations acting on the slow variables. We analytically prove that the coupling of two identical neurons preserves the emergence of Devaney chaos through the existence of a generalized snap-back repeller, provided that a snap back repeller exists for the original system. We present numerical simulations for the coupling of two different neurons showing the arising of a potential global strange attractor, whose fractal structure is strongly suggested by the computation of a non-integer Kaplan-Yorke dimension. Furthermore, we perform standard numerical studies concerning time series, Lyapunov exponents spectra, bifurcation diagrams and basins of attraction. Finally, we briefly propose a generalization of the coupling to an arbitrary number of neurons.
Comments29 pages, 19 figures. This version contains substantial revisions to the analytical part of the paper. Lemma 1 and Theorem 3 from the previous version have been removed as incorrect. Theorem 4 has been reformulated, while preserving an analogous main result. The numerical results and simulations are unchanged
