Abstract: We have investigated synchronization phenomena of chaotic circuits with transmission lines coupled by parallel transmission lines located in the same direction or reverse direction. In this study, we investigate two Chua’s circuits with transmission lines located in opposite direction when the lines are coupled by resistors. Keyword Chaotic circuits, Chua’s circuit, Transmission lines, Chaos synchronization 1. まえがき 信号回路などの動作周波数の超高速化に伴い、回路 内の配線を伝送線路として取り扱う必要性が高まって いるが、カオスなどの不規則性をもつ信号が、伝送線 路を通した結合によりどのような影響を受けるかにつ いてはほとんど調査されていない.我々は、過去の研 究において、伝送線路を含むカオス回路が、線路のク ロストークによる結合により、どのような同期現象を 発生するかについて調査してきた.クロストーク結合 を L と C による結合でモデル化したときに、回路の向 きが同じ向きでも逆向きでも、結合する強さにより回 路同士が、同相同期や逆相同期で同期する場合がある ことを確認している [1][2]. 本研究では、伝送線路を含むカオス回路を逆向きに 配置し、線路を抵抗のみで結合したときに、どのよう な同期現象が見られるかを計算機シミュレーションに より調査する.さらに、結合の位置と数を変化させた ときに、同期がどのように変化するのかについても調 査を行う. 2. 伝送線路を含むカオス回路 今回の計算機シミュレーションでは、チュア回路の LC 共振回路を伝送線路で置き換えた回路を基本回路 モデルとした. 図1.チュア回路と非線形素子の電圧電流特性 f(v) = { m1(v − E) + m0E (v > E) m0v (|v| ≤ E) m1(v + E) − m0E (v < E) } 伝送線路の等価回路を10段のキャパシタとイン ダクタのラダー回路で近似すると、図2のようになる. 図2.伝送線路を含むチュア回路の等価回路 C0 dv0 dt = −G0(v0 − v1) − f(v0) CS dvk dt = ik−1 − ik (k = 1, 2, ⋯ 10) LS dyk dt = vk − vk+1 f(v0) = m1v0 − (m0 − m1) ∙ |v0 − E| − |v0 + E| 2 3. 逆向きに抵抗結合した伝送線路を含むカオ ス回路 図3に、本研究で対象とする伝送線路を含むチュア 回路の逆向き抵抗結合モデルを示す. 図3.伝送線路を含むチュア回路の等価回路の抵抗結合モデ ル

Abstract: Abstract Studies on synchronization phenomena are extensively carried out in various fields. Recently, in particular, synchronization phenomena in chaotic circuits are studied many researchers. Chaos phenomena are quite dependent on initial values and not periodical and predictable. Moreover, the synchronization phenomena have caused very interesting phenomena. Synchronization and the related bifurcation of chaotic systems are good methods to describe various higher-dimensional nonlinear phenomena in the field of natural science. In this study, we investigate synchronization phenomena observed in a ring of simple chaotic circuits cross-coupled via inductors. Interesting synchronization phenomena can be confirmed by computer simulations.

Abstract: In this study, a ring of coupled simultaneous oscillators with two LC resonators is investigated. By computer simulations, asynchronous oscillations of double-mode and N -phase are confirmed to be stably generated. Careful observation reveals various interesting synchronization phenomena which have not reported before.

Abstract: Stochastic resonance (SR) is a phenomenon where dynamic noise is effectively used to induce state transitions in a double-well potential system driven by subthreshold external forces. The noises are given to the system as an additional force. Recently, a phenomenon called “chaotic resonance” (CR) has been spotlighted in the literature. CR can be observed in chaotic systems which have multiple strange attractors, and have ability to accept external forces to cause transitions between the attractors. In such chaotic systems, chaotic fluctuations, instead of additional noises in SR systems, could effectively be used to cause the attractor transition, which may result in CR under certain parameter conditions; i.e., such CR systems do not require any external noise source, unlike traditional SR systems. In this research, we employed Chua’s oscillator as a possible candidate of CR systems. The oscillator was driven by a sinusoidal voltage source as a subthreshold driving force. In a certain range of the driving force frequencies, we observed chaotic transitions between two operational regions, whereas no transition between the operational regions was observed in the other frequency range, which indicated that chaotic fluctuation certainly assisted the state transition. Furthermore, we observed nonmonotonic CR characteristics (correlation value and signal-to-noise ratio between the driving force and the output signal) that correspond to typical nonmonotonic SR curves. And then, we evaluated an array of forced Chua’s oscillators, just like in the single Chua’s oscillator and observed the network will enhance correlation value and SNR in CR.

Abstract: Neurogenesis is that new neurons are generated in the human brain. We focus on the characteristic of the neurogenesis with biologically. In the previous study, we have proposed artificial network model which was applied the neurogenesis to Multi-Layer Perceptron (MLP). In this study, we show the effectiveness of the proposed network with neurogenesis for pattern recognition. And we investigate the parameter dependency for detailed research on the influences of neurogenesis on MLP.

Abstract: Relationship between Oscillatory Phenomena and Eigenvalues in Cellular Neural Networks Using Two Kinds of Cloning Templates Yasuteru HOSOKAWA† and Yoshifumi NISHIO†† † Faculty of Management and Information Science, Shikoku University Furukawa, Ohjin-cho, Tokushima-shi, Tokushima 771–1192 Japan †† Faculty of Engineering, Tokushima University 2–1 Minami-Josanjima-Cho, Tokushima-shi, Tokushima 770–8506 Japan E-mail: †hosokawa@keiei.shikoku-u.ac.jp, ††nishio@ee.tokushima-u.ac.jp