# Behavioral Modeling of Memristor-Based Rectifier Bridge
## 1 Introduction  
Recently, the element base for the designing of nonlinear dynamic devices is changed due to the emergence of elements with new properties and technologies for their creation. More and more devices are synthesized based on memristors or memristive structures [1, 2, 3, 4]. This process results from the effective characteristics of a memristor as a passive electrotechnical element. The memristor possesses the following useful properties [1, 2, 3, 4]:  
* Being an analog element, its resistance can take any values. This is a positive property in comparison with any binary element whose value can be either 0 or 1. Such variability of resistance is realized in one element, the memristor size is reduced to several nanometers and the response rate is reduced to nanoseconds. * The memristor does not store a charge. This means that it is not prone to charge leaks, which must be dealt with when going to nanometer-scale microcircuits. * The memristor is a non-volatile element, and data can be stored as long as the materials from which it is made exist. * Memristors placed on crossing conductors (crossbars) can be used to form densely packed memory. * Many memristor materials are compatible with complementary metal-oxide-semiconductor (CMOS) technology. A memristor was theoretically described first by [PERSON] in 1971 [5]. There were a lot of investigations devoted to elements with resistive switching [6, 7, 8, 9, 10, 11] and only in 2008 the link between resistive switching and the theory of memristors was established in the Hewlett Packard (HP) laboratory [12]. In [12] the authors represented a variant of the ideal memristor model, which doesn't completely describe any resistive switching element [13]. Nowadays, memristive systems lead to building non-volatile storage devices [14; 15], self-adjusting analog-digital control devices [14; 15], hardware security [16], in-memory computing [17], programmable logic systems [18; 19], neuromorphic systems [20; 21], image converters [22], different types of neural networks, for instance, multi-layer feedforward, radial basis, recurrent, cellular, convolutional, neuro-fuzzy networks [23; 24; 25; 26], and, undoubtedly, analog devices for various purposes (oscillators, chaotic circuits, amplifiers with a variable coefficient, comparators, Schmitt trigger, rectifiers, etc.) [27; 28; 29]. The mentioned advantageous diversity of the application fields is caused by using different materials and technologies for designing of memristors. Memristors can be made of a metal-isolator-metal (MIM) sandwich based on transition metal oxides such as TiO\({}_{2}\), NiO\({}_{2}\), CuO, HfO\({}_{2}\), etc. These memristors are called resistive ones due to the capability of resistance switching. In majority cases, other memristors are fabricated as spintronic, organic (polymeric) and ferroelectric ones [30]. However, the mentioned aspect has a negative effect that consists in the great variety of mathematical memristor models. These models describe different physical processes in memristors. As a result, we have to face the challenge of using mathematical memristor models, which essentially depend on the specifics of materials and technologies. These difficulties emerge on modeling memristor-based devices too. The way of overcoming the mentioned challenges is the modeling of memristors and memristor-based devices on the input/output approach, which proposes to build a behavioral model on using the assigned sets of the input and output signals of a device represented as a nonlinear dynamic system. According to this approach the device is considered to be a \(\Leftrightarrow\)black box\(\Leftrightarrow\) and we construct its general mathematical model without taking into account the internal parts of the device. This view is appropriate and effective when a general model cannot be synthesized by means of the component models (there is no sufficient description of the structure or components of the device), as well as when the device is a part of more complicated constructions.