Asai Y, Nomura T, Sato S
Graduate School of Engineering Science, Osaka University, Toyonaka, Japan.
Biosystems. 2000 Oct-Dec;58(1-3):239-47. doi: 10.1016/s0303-2647(00)00128-3.
Bifurcations of periodic solutions in a model of weakly coupled two Bonhoeffer-van der Pol equations are studied. The model realizes a half-center model with reciprocal inhibition, a typical model used in the field of neural motor control to account for the generation of alternating rhythmic bursts observed in motoneurons and spinal neural networks. Several oscillatory solutions such as in-phase, anti-phase as well as out-of-phase solutions emerge from the model's equilibrium as one of the parameters of the model changes. Among the variety of bifurcations exhibited by the model, we analyze Hopf bifurcations, by which several periodic solutions emerge, and illustrate generation mechanisms of alternating oscillations in the model.
研究了弱耦合的两个邦霍夫-范德波尔方程模型中周期解的分岔。该模型实现了一个具有相互抑制的半中心模型，这是神经运动控制领域中用于解释在运动神经元和脊髓神经网络中观察到的交替节律性爆发产生的典型模型。随着模型参数之一的变化，该模型的平衡点会出现几种振荡解，如实相位、反相位以及异相位解。在该模型所展示的各种分岔中，我们分析了霍普夫分岔（通过该分岔出现了几个周期解），并阐明了该模型中交替振荡的产生机制。
