基于变参神经动力学方法的分形生成方法研究

作     者：阿克林（Akram Ahmad） 

作者单位：华南理工大学 

学位级别：硕士

导师姓名：张智军

授予年度：2019年

学科分类：07[理学] 08[工学] 081104[工学-模式识别与智能系统] 070104[理学-应用数学] 0701[理学-数学] 0811[工学-控制科学与工程] 

摘      要：To solve static and time-varying non-linear complex-valued equations by neural dynamics,using two new kinds of varying-parameters discrete-time complex-valued neural dynamics（VP-DTCVND）,the two models has proposed and analysed.Different from fixedparameters discrete-time complex-valued neural dynamics（FP-DTCVND）,VP-DTCVND is based on monotonically increasing time-varying design-parameters.In this dissertation,new fractals have yielded by using the two VP-DTCVND models via solving static and time-varying nonlinear equations in the complex domain,for generating new unique fractals.Exponential-type and power-type VP-DTCVND apply four different kinds of activation functions（i.e.,linear,power-sum,power-sigmoid and hyperbolic-sine activation functions）,and these activation functions have been introduced and used to create various neural fractals.The proposed VP-DTCVND can determine static and time-varying non-linear equations,unlike Newton iterations which only can solve static non-linear equations.Fractals yielded are different from Newton fractals;the fractals generated are unique of their classifications.Varieties of equations are solved to show different fractals and approve the validity of the proposed models.Computer simulation results based on different activation functions demonstrate that the VP-DTCVND models can serve as new algorithm to generate new fractals.Comparisons between FP-DTCVND fractals and VP-DTCND fractals finally presented to verify the uniqueness of the proposed two new models in generating fractals.The effectiveness of the VP-DTCVND models using different activation functions for solving time-varying nonlinear complex equations reflected.