This thesis proposes a novel model that accurately captures the asymmetric hysteretic behavior of memristive devices exhibiting self-crossing hysteresis loops. The proposed model combines the Bouc-Wen Baber-Noori model with other non-linear elements in the resistive switching process. Existing models for memristive behavior, including physical-based memristive models, phenomenological-based models, and models that employ stochastic techniques, are reviewed. The Bouc-Wen model is significant for predicting the current-voltage outputs within memristors, and a new phenomenological model is presented that incorporates the modified Bouc-Wen-Baber-Noori model, a nonlinear geometric-based equation, and bilinear optimization to predict the response of a memristive system. The potency of the proposed model is demonstrated by a dynamic simulation of a memristor system in relation to an integrated circuit system. The proposed model provides reliable predictions of the hysteretic behavior of memristive devices, enabling their efficient use in future computing applications. The thesis provides insights into the development of accurate and efficient models for the hysteretic behavior of memristive devices, which will facilitate their widespread use in various engineering applications.