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本文以驱动项只对正差分起作用,而对负差分不起作用且有时滞的三阶非线性差分方程y(K+3)=P_1y(K+2)P_2y(K+1)+P_3y(K)+P_4ω[u(K+1-K_(?))-u(K-K_(?))]作为瞳孔光脉冲响应动态过程的数学模型.其中y 为瞳孔面积的改变量,u 为输入光强的改变量,P_1、P_2、P_3、P_4均为参数,K_(?)为一与时滞有关的参数.ω为下列非线性算子:(?)采样间隔取为0.1秒.作者根据在不同宽度和不同极性(增亮或减暗)的方波光强刺激下瞳孔面积变化的实验数据,用单纯形法在计算机上估算出了上述方程的各个参数.根据此模型与由此估算得出的参数算得的理论曲线与实验数据吻合得很好,并且在一定范围内与刺激方波的宽度和极性无关.这表明这个模型确实可以表征瞳孔光脉冲响应的动态规律.
In this paper, the third-order nonlinear difference equation (K + 3) = P_1y (K + 2) P_2y (K + 1) + P_3y K is the mathematical model of dynamic process of pupil light impulse response, where y is the change of pupil area, u is the input of K (K + 1-K_ (?)) - u K_ (?) Is a parameter related to the time delay, ω is the following nonlinear operator: (?) The sample interval is taken as 0.1 second. According to the author, according to the change of light intensity, P_1, P_2, P_3, P_4 are all parameters, The experimental data of pupil area change under square wave light intensity stimulation with different widths and different polarities (increase or decrease the darkness) are used to calculate the parameters of the above equations by the simplex method. According to this model and the estimated The theoretical curve calculated by the parameters is in good agreement with the experimental data and is independent of the width and polarity of the stimulated square wave within a certain range, which shows that this model can indeed characterize the dynamic law of pupil light impulse response.