Over the past decade, significant advancements have been made in the study of silicon nanowires (SiNWs). These nanoscaled devices can exhibit a memristive type of hysteresis in the current/voltage (I/V) plane that has been utilized in the biosensors leading to exceptional sensitivities up to the femto levels. Here we investigate the memristive properties of SiNW-based biosensors in their unmodified state, as well as after surface biofunctionalization with aptamers. The development of SiNWs involved a top-down nanofabrication approach, resulting in nanowires with 100 nm wide and 1 mu m long. Later, biofunctionalization was performed through controlled drop casting. The experimental findings obtained in this study demonstrate for the first time that different SiNWs from the same fabrication batch can exhibit diverse memristive switching phenomena in the I/V plane. These phenomena encompass both volatile noncrossing memristive behavior as well as nonvolatile crossing memristive responses. Furthermore, we demonstrate that the I/V hysteresis exhibited by biofunctionalized nanowires is determined by their inherent memristive characteristics and the induced capacitive effect. Drawing upon these new findings, a simple mathematical simulation model of the Memristive biosensor is developed and evaluated in SPICE.