著者

Yota Tsukamoto Honami Tsushima Tohru Ikeguchi

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.13, no.2, pp.367-372, 2022 (Released:2022-04-01)

参考文献数

9

被引用文献数

3

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In the field of neuroscience, it is widely acknowledged that neurons exhibit periodic, quasi-periodic, and chaotic responses to periodic inputs. In this study, we evaluated the responses of the Izhikevich neuron model stimulated by sinusoidal inputs. First, we analyzed the dynamical behavior of the Izhikevich neuron model to the sinusoidal inputs in the state space and found two types of responses: periodic and non-periodic. Next, we obtained the domains of the periodic and non-periodic responses on the frequency-amplitude plane of the sinusoidal inputs by evaluating the diversity index of the inter-spike intervals. Finally, we analyzed the responses of the Izhikevich neuron model using the stroboscopic plot. Consequently, we clarified that a periodic response is a limit cycle and an irregular response is a torus, which implies that the irregular responses of the Izhikevich neuron model stimulated by sinusoidal inputs are quasi-periodic responses.

著者

Kazuya Sawada Yutaka Shimada Tohru Ikeguchi

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.13, no.2, pp.385-390, 2022 (Released:2022-04-01)

参考文献数

22

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State space reconstruction using time-delay coordinate systems is the most effective and significant technique for analyzing complex time series generated by nonlinear dynamical systems. In this study, we investigated the relationships between reconstruction parameters and the similarity of the structural properties of original and reconstructed attractors. In particular, we investigated the similarities between inter-point distance distributions on original and reconstructed attractors, while varying the reconstruction parameters for reconstructing a dynamical system using a time-delay coordinate system. The results show that the product of the reconstruction dimension and the time-delay should be constant to obtain high similarity.

著者

Yota Tsukamoto Honami Tsushima Tohru Ikeguchi

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.14, no.4, pp.677-690, 2023 (Released:2023-10-01)

参考文献数

29

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The Izhikevich neuron model can reproduce various types of neurons, including chaotic neurons, by utilizing appropriate parameter sets. This study analyzes the responses of a periodically forced Izhikevich neuron with chaotic parameters using three measures—the diversity index, the coefficient of variation, and the local variation—to quantify interspike intervals (ISIs). The evaluation of ISIs combining these three measures clarifies the differences in neuronal activities, but evaluation using an individual measure cannot. In addition, we analyzed the change in the stability of the equilibrium points caused by a periodic input on a phase plane. The results indicate that in electrophysiologically feasible parameter sets, the stability of equilibrium points plays a crucial role in determining the critical amplitude around which irregular activities transition to regular ones. Thus, the relationship between neural behavior and the period and amplitude of the input current is contingent upon the existence and stability of equilibrium points.

著者

Kihei Magishi Tomoko Matsumoto Yutaka Shimada Tohru Ikeguchi

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.13, no.2, pp.343-348, 2022 (Released:2022-04-01)

参考文献数

22

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Word co-occurrence networks (WCNs) are a major tool used to analyze languages quantitatively. In a WCN, the vertices are words (morphemes), and the edges connect n consecutive words in a sentence on the basis of the n-gram. Most studies use WCNs transformed at n=2. In this study, we investigated the changes in the structural features of WCNs when n increases using four types of documents for eight languages. We found that WCNs with n≧ 3 reflect features of the languages that do not appear when n = 2 and that some structural features evaluated by network measures depend on the text data.