Memristor is a name of passive two-terminal circuit elements in which there is a functional relationship between charge and magnetic flux linkage. Memristor theory was formulated and named by Leon Chua in a 1971 paper. In 2008, a team at HP Labs announced the development of a switching memristor based on a thin film of titanium dioxide. It has a regime of operation with an approximately linear charge-resistance relationship as long as the time-integral of the current stays within certain bounds. These devices are being developed for application in nanoelectronic memories, computer logic, and neuromorphic computer architectures.
A memristor is a passive two-terminal electronic component in which there is a functional relationship between charge and magnetic flux linkage. When current flows in one direction through the device, the resistance increases; and when current flows in the opposite direction, the resistance decreases, although it must remain positive. When the current is stopped, the component retains the last resistance that it had, and when the flow of charge starts again, the resistance of the circuit will be what it was when it was last active.
More generally, a memristor is a two-terminal component in which the resistance depends on the integral of the input applied to the terminals (rather than on the instantaneous value of the input as in a varistor). Since the element "remembers" the amount of current that has passed through it in the past, it was tagged by Chua with the name "memristor." Another way of describing a memristor is that it is any passive two-terminal circuit elements that maintains a functional relationship between the time integral of current (called charge) and the time integral of voltage (often called flux, as it is related to magnetic flux). The slope of this function is called the memristance M and is similar to variable resistance. Batteries can be considered to have memristance, but they are not passive devices. The definition of the memristor is based solely on the fundamental circuit variables of current and voltage and their time-integrals, just like the resistor, capacitor, and inductor. Unlike those three elements however, which are allowed in linear time-invariant or LTI system theory, memristors of interest have a nonlinear function and may be described by any of a variety of functions of net charge. There is no such thing as a standard memristor. Instead, each device implements a particular function, wherein the integral of voltage determines the integral of current, and vice versa. A linear time-invariant memristor is simply a conventional resistor.
In his 1971 paper, memristor theory was formulated and named by Leon Chua, extrapolating the conceptual symmetry between the resistor, inductor, and capacitor, and inferring the memristor was a similarly fundamental device. (However, as mentioned above, if it has no non-linearity then it is the same as a standard resistor. It is more meaningful to compare it with a varistor, which has a non-linear relationship between current and voltage.) Other scientists had already proposed fixed nonlinear flux-charge relationships, but Chua's theory introduced generality.
Like other two-terminal components (e.g., resistor, capacitor, inductor), real-world devices are never purely memristors ("ideal memristor"), but will also exhibit some amount of capacitance, resistance, and inductance. Note however that a "memristor" with constant M and a resistor with constant R (i.e. not a varistor) are the same thing.
Williams' solid-state memristors can be combined into devices called crossbar latches, which could replace transistors in future computers, taking up a much smaller area.
They can also be fashioned into non-volatile solid-state memory, which would allow greater data density than hard drives with access times potentially similar to DRAM, replacing both components. HP prototyped a crossbar latch memory using the devices that can fit 100 gigabits in a square centimeter, and has designed a highly scalable 3D design (consisting of up to 1000 layers or 1 petabit per cm3). HP has reported that its version of the memristor is currently about one-tenth the speed of DRAM. The devices' resistance would be read with alternating current so that the stored value would not be affected.
Some patents related to memristors appear to include applications in programmable logic, signal processing, neural networks, and control systems.
Recently, a simple electronic circuit consisting of an LC network and a memristor was used to model experiments on adaptive behavior of unicellular organisms. It was shown that the electronic circuit subjected to a train of periodic pulses learns and anticipates the next pulse to come, similarly to the behavior of slime molds Physarum polycephalum where the viscosity of channels in the cytoplasm respond to periodic changes of environment. Such a learning circuit may find applications, e.g., in pattern recognition. The DARPA’s SyNAPSE project has funded HP Labs, in collaboration with the Boston University Neuromorphics Lab, to develop neuromorphic architectures which may be based on memristive systems. In 2010, Massimiliano Versace and Ben Chandler co-wrote an article describing the MoNETA (Modular Neural Exploring Traveling Agent) model. MoNETA is the first large-scale neural network model to implement whole-brain circuits to power a virtual and robotic agent compatibly with memristive hardware computations. The software used to implement MoNETA, Cog Ex Machina, has been featured on the cover page of IEEE Computer in February 2011 in a joint article by HP Labs and the Boston University Neuromorphics Lab.