wileyonlinelibrary.comspike-timing-dependent plasticity (STDP) using various types of memristors. [ 12,[16][17][18][19][20][21] However, in these studies, the synaptic learning rules were implemented phenomenologically by engineering the duration or amplitude of the overlapping programming pulses from the pre-and postsynaptic neurons. [ 12,[18][19][20][21][22] The phenomenological nature of this approach means that different programming pulses have to be manually designed to implement the desired synaptic behaviors. However, in biology, the apparently different learning rules have been shown to be specifi c effects driven by internal molecular dynamic processes under stimulation. [23][24][25] Consequently, manually designing a system to specifically target only certain effects, but not their cause, can easily miss other important aspects that make the system functional.In a previous study, we showed that by employing multiple internal state variables (e.g., temperature and conduction fi lament size), a second-order memristor can be obtained which allows biorealistic implementation of several synaptic learning rules-notably spike-timing-dependent plasticity. [ 26 ] Here, we show that a second-order memristor can also be implemented by utilizing the different time scales of internal ionic dynamics in oxide-based memristors, leading to the natural implementation of several types of important synaptic behaviors. We show that an oxide-based memristor may be described by two state variables-one ( w c ) directly determines the device conductance (weight) and the other ( w m ) affects the dynamics of the fi rst (conductance) state variable. Specifi cally in our device system, w c represents the area of the conducting channel region in the oxide memristor thus directly affecting the device conductance, while w m represents the oxygen vacancy mobility in the fi lm which directly affects the dynamics of w c but only indirectly modulates the device conductance. Within this secondorder memristor framework, the device long-term state can be shown to be controlled by activities at much shorter time scales. Specifi cally, the natural decay of the state variable w m provides an internal timing and modulation mechanism analogous to that exhibited by Ca 2+ concentration, [23][24][25] and enables the memristor to exhibit important rate-and timing-dependent behaviors at both short-term such as pair-pulse facilitation (PPF) [ 27 ] and long-term such as STDP [ 28 ] using simple, nonoverlapping spike signals. The experimental observations can in turn be quantitatively explained using a simple dynamic device model including the two state variables, and facilitates large-scale simulation and implementation of memristor-based neuromorphic systems.Memristors have attracted broad interest as a promising candidate for future memory and computing applications. Particularly, it is believed that memristors can effectively implement synaptic functions and enable effi cient neuromorphic systems. Most previous studies, however, focus on implementin...