Memristive technology has been widely explored, due to its distinctive properties, such as nonvolatility, high density,versatility, and CMOS compatibility. For memristive devices, a general compact model is highly favorable for the realization of its circuits and applications. In this paper, we propose a novel memristive model of TiOx-based devices, which considers the negative differential resistance（NDR） behavior. This model is physics-oriented and passes Linn＇s criteria. It not only exhibits sufficient accuracy（IV characteristics within 1.5% RMS）, lower latency（below half the VTEAM model）,and preferable generality compared to previous models, but also yields more precise predictions of long-term potentiation/depression（LTP/LTD）. Finally, novel methods based on memristive models are proposed for gray sketching and edge detection applications. These methods avoid complex nonlinear functions required by their original counterparts. When the proposed model is utilized in these methods, they achieve increased contrast ratio and accuracy（for gray sketching and edge detection, respectively） compared to the Simmons model. Our results suggest a memristor-based network is a promising candidate to tackle the existing inefficiencies in traditional image processing methods.
