Mathematical Modeling Of Threshold Switches For Stepwise Behavior Response Of Aquatic Organisms Under Environmental Stress

Behavior monitoring is an important way to characterize the current quality of environment,which is mostly used in water quality assessment.In our laboratory,a mathematical model was established to express the relationship between environmental stress and behavior of aquatic organisms in the prophase,considering the comprehensive effects and environmental stress of various pollutants and concentrations.However,a great problem is that the time that defined as a boundary between two stages can not be determined by mathematical model.When the stage should be switched can only be determined by manual delimitation currently.In addition,as the position of threshold switch can not be automatically determined by mathematical modeling,the model can never be used in real-time monitoring.In order to solve these problems,this study firstly collects the data of zebrafish behavior strength under Atrazine stress,then finds the regular pattern of threshold related to behavior strength trends,next defines the initial threshold screening domain,stage switch threshold screening domain and interference point screening rules,and constructs a vector-based fuzzy inflection point extraction algorithm based on these threshold screening rules.The inflexion points are selected according to the data,and then the threshold rules are applied to obtain all the threshold points in the current behavioral strength data.Final results show that the screening results of this model are basically consistent with those of manual screening.The following problem is how to apply the result in real-time monitoring,especially the judgment of the current time point.It's impossible to obtain the status of current point without future data,so we use the time series analysis model-ARIMA model to predict the future short-term data.This model is usually applied to the short-term and medium-term prediction of non-stationary time series.The most suitable ranks are found by minimum AIC and BIC rules from a given range,and the parameters of the model are fitted with the existing historical series.The data of the next 30 time points are predicted by the fitted model,and the threshold points in the prediction results are judged by the threshold screening algorithm.The experimentalresults show that the model can effectively predict the short-term trend change of behavior strength,and the location of the predicted threshold points is consistent with the real data.In addition,the RSOM model is introduced to validate the ascription of threshold points,which used to confirm the prediction results.RSOM is upgraded to deal with time series problems based on traditional SOM algorithm.Firstly,the neuron weight matrix of the model is trained by inputting a large number of existing threshold data,and the trained weight matrix is retained.Then the results are clustered.The results show that RSOM can accurately represent all the threshold points in the same cluster.So when the prediction threshold point is obtained,the related data of the point can be input into the trained weight matrix to know the location of the neuron to which the point belongs,and then to know whether the point belongs to the category of the threshold point.The experimental results show that the validation method is effective and feasible.In this study,three main algorithms are used to construct a mathematical model to automatically screen and verify the position of threshold switch for behavioral strength data.The value of threshold switch can be applied to the Stepwise Behavioral Response Mathematical Model,and then the whole model can be connected,which lays a foundation for seamless switching of behavioral strength expression and provides conditions to create a real-time monitoring system for aquatic organisms.