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In the memristive version of a standard space-invariant Cellular Nonlinear Network, each cell accommodates one first-order non-volatile memristor in parallel with a capacitor. In case, the resistance switching memory may only undergo almost-instantaneous switching transitions between two possible resistive states, acting at any time, as either the on or the off resistor, the processing elements effectively operate as first-order dynamical systems, and the classical Dynamic Route Map technique may be applied to investigate their operating principles. On the contrary, in case the memristors experience smooth conductance changes, as the bioinspired array implements memcomputing paradigms, each cell truly behaves as a second-order dynamical system. The recent extension of the Dynamic Route Map analysis tool to systems with two degrees of freedom constitutes a powerful technique to investigate the nonlinear dynamics of memristive cellular networks in these scenarios. This paper exploits this system-theoretic technique, called Second-Order Dynamic Route Map, to introduce a novel systematic procedure to design memristive arrays, in which a given memcomputing task is executed by ensuring that, depending upon the network inputs and initial conditions, the analogue dynamic routes of the states of the processing elements, namely capacitor voltages and memristor states, asymptotically converge toward pre-defined stable equilibria. [ABSTRACT FROM AUTHOR]

This paper presents the theory of a novel memcomputing paradigm based upon a memristive version of standard Cellular Nonlinear Networks. The insertion of a nonvolatile memristor in the circuit of each cell endows the dynamic array with the capability to store and retrieve data into and from the resistance switching memories, obviating the current need for extra memory blocks. Choosing the parameters of each cell circuit so that the memristors may undergo solely sharp transitions between two states, each processing element may be approximately described at any time as one of two first-order systems. Under this assumption, the classical Dynamic Route Map may be employed to synthesise and analyse the data storage and retrieval genes. A new system-theoretic methodology, called Second-Order Dynamic Route Map, is also introduced for the first time in this paper. This technique allows to study the operating principles of arrays with second-order processing elements, as is the case, in the proposed network, if the set up of cell circuit parameters induces analogue memristive dynamics. This paper shows how the novel tool may be adopted to investigate the operating mechanisms of a cellular array with second-order cells, which compute the element-wise logical OR between two binary images. [ABSTRACT FROM AUTHOR]

This work presents a detailed study of the nonlinear dynamics of a tantalum oxide memristor recently fabricated at Hewlett Packard Labs. Our investigations uncover direct current, quasi-static, and alternating current behavior of the nanodevice. A thorough study of the dynamics emerging in the nanoscale element under various input/initial condition combinations reveals a fundamental property of the tantalum oxide device, which was unnoticed so far. The initial condition has no effect on the steady-state operation of the memristor under non-zero input. This property, known as fading memory in system theory, implies the uniqueness of asymptotic behavior of the memristor. The progressive input-induced memory erase phenomenon is solely determined by the switching dynamics of the nanodevice, mathematically described by the state evolution function, which governs the rate of evolution of the memristor state. A constant-sign DC input will activate on or off switching dynamics only. Consequently, due to the limited on/off memductance ratio, the memristor will asymptotically attain a fully-conducting or highly-resistive state, irrespective of the initial condition. Most interestingly, under AC periodic excitations, it is the pronounced asymmetry in the state dependence of on and off switching processes which is at the basis of the reported history erase effect. It is important to point out that this novel fading memory phenomenon does not compromise the nonvolatile behavior of the nanostructure. In fact, despite the device may be stimulated so as to forget its past history, it still has a continuum of analog nonvolatile memory states. [ABSTRACT FROM PUBLISHER]

The main focus of this paper is the evolution of complex behavior in a system of coupled nonlinear memristor circuits depending on the applied coupling conditions. Thereby, the parameter space for the local activity and the edge-of-chaos domain will be determined to enable the emergence of the pattern formation in locally coupled cells according to Chua’s principle. Each cell includes a Niobium oxide-based memristor, which may feature a locally active behavior once it is suitably biased on the negative differential resistance region of its DC current-voltage characteristic. It will be shown that there exists a domain of parameters under which each uncoupled cell may become locally active around a stable bias state. More specifically, under these conditions, the coupled cells are on the edge-of-chaos, and can support the static and dynamic pattern formation. The emergence of such complex spatio-temporal behavior in homogeneous structures is a prerequisite for information processing. The theoretical results are confirmed by measurements as well as by the numerical simulations of the accurate device and circuit models. [ABSTRACT FROM AUTHOR]

We present a compact, continuous, and numerically stable version of a tantalum oxide (TaOx) memristor model which can be employed for robust and reliable simulations of large scale memristor based circuits. The original model contains a piecewise differentiable function in the memductance expression and discontinuous step functions in the state equation. Additionally, the original model does not set a proper upper bound for the state variable and may admit blowing up solutions due to an exponential power term, preventing the use of it for numerically reliable simulations. Considering these drawbacks, we modify the original model so as to i) simplify the memductance function while removing its piecewise differentiable nonlinearity, ii) include a proper window function for the ON state dynamics, which is missing in the original model, iii) modify and bound the exponential power term to prevent an uncontrollable blow-up of the solutions, and iv) apply a process called unification, allowing us to remove the step functions inherent in the model, which is a novelty in state-limited memristor models. We validate the accuracy of the proposed model via DC and transient simulations, dynamic route map analysis and a Spice implementation of an anti-series configuration, showing the applicability of the model. [ABSTRACT FROM AUTHOR]