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Canard phenomenon in second-order autonomous unijunction transistor circuit

机译：二阶自主单结晶体管电路中的Canard现象

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In the nonlinear dynamic system the chaotic phenomenon can only appear in the autonomous system whose order is higher than three (included), which impels the research work in the nonlinear field to focus on the above-mentioned system. However, very complex dynamic phenomenon may also occur in the second-order autonomous system. Eckhaus reported first the Canard phenomenon in their mathematics notes, and sometime later Braaksma et al. reported the Canard phenomenon appearing in the equation of the cell membrane. The term of "Canard" originated from the phase trajectory taking the shape of a French duck. A brief description about its generation process is given as follows: for the second-order autonomous system consisting of a nonlinear function f(x),in the vicinity of the bifurcation point of the control parameter, the phase diagram of the system may have a limit cycle with the shape of a duck. Following the variation of the control parameters, the duck will lose its head (at this time the limit cycle is constructed by a jumping straight line and two portions of the curve describing f(x)), or gain its head (formed by two jumping straight lines and two segments of the curve describing f(x) with opposite slopes). The limit cycle of relaxation oscillation (formed by two jumping straight lines and two portions of the curve describing f(x) with the same slopes) is shown in fig. 1. A unijunction transistor (UJT) has been adopted to construct the second-order autonomous circuit, where many characteristics similar to and different from those given in refs. have been revealed.
机译：在非线性动力系统中，混沌现象只能出现在阶数高于三（包括）的自治系统中，这促使非线性领域的研究工作集中在上述系统上。但是，在二阶自治系统中也可能会发生非常复杂的动态现象。 Eckhaus在他们的数学笔记中首先报道了Canard现象，后来又报道了Braaksma等。报道了在细胞膜方程中出现的Canard现象。 “鸭嘴”一词起源于呈法国鸭形的相轨迹。对其产生过程的简要说明如下：对于由非线性函数f（x）组成的二阶自治系统，在控制参数的分叉点附近，系统的相图可能具有一个用鸭子形状限制循环。随着控制参数的变化，鸭子将失去头部（此时，极限循环由一条跳跃的直线和描述f（x）的曲线的两部分构成），或获得其头部（由两次跳跃形成）直线和曲线的两段，以相反的斜率描述f（x）。松弛振荡的极限循环（由两条跳跃的直线和描述f（x）的曲线的两个部分以相同的斜率形成）显示在图5中。 1.采用单结晶体管（UJT）构成二阶自主电路，该电路的许多特性与参考文献中给出的特性相似或不同。已被揭露。

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