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Given the high saturation, strong nonlinearity, and tight coupling characteristics of the magnetic paths in a switched reluctance motor (SRM), accurately modeling flux-linkage is challenging, thus leading to excessive torque ripple during SRM torque control. In order to enhance the precision of the SRM flux-linkage model, a neural network-based method for the parameter identification of SRM's nonlinear flux-linkage model was proposed in this study. Logistic mapping elements were incorporated into the feedback layer of the diagonal recurrent neural network (DRNN), and chaotic control parameters were designed. Then, the construction of an analytical model of the nonlinear exponential flux-linkage function using the chaotic diagonal recurrent neural network (CDRNN) was established. By utilizing sample data of flux-linkage, current, and angular position, the parameters of this model were estimated, thus achieving a precise nonlinear exponential function model of the flux-linkage. Results show that, the integration of logistic mapping in the CDRNN feedback layer effectively prevents the local minima typically associated with conventional DRNN. The maximum error in the identified flux-linkage is less than 0.01 Wb, and the accuracy reached 95%. Compared with the DRNN method, the CDRNN approach demonstrates significantly reduced errors and higher model precision. This study offers valuable insights for enhancing the performance of SRM torque ripple control. [ABSTRACT FROM AUTHOR]