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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]

The seizure prediction problem has been addressed by many researchers from very different fields for more than three decades. The vision of an implantable seizure prediction device may become reality soon: the first clinical study of such a device has been realized very recently and other realizations are not far behind. Cellular Nonlinear Networks (CNN) were firstly introduced by Chua and Yang in 1988 and later extended to an inherently parallel processing framework called the CNN Universal Machine (CNN-UM). This framework combines high computational power with low power consumption and miniaturized design—making it a very promising basis for the realization of a seizure warning device. In this contribution, we compare the seizure prediction performance of an eigenvalue based PCA-preprocessing followed by a nonlinear CNN signal prediction to the performance of a linear signal prediction approach followed by a level-crossing behavior analysis as well as to the performance of a combination of the two methods. [ABSTRACT FROM AUTHOR]

If the memristor, used in each cell of a memristive variant of the standard space-invariant Cellular Nonlinear Network (CNN), undergoes analogue memductance changes, the processing element operates as a second-order system. The Dynamic Route Map (DRM) technique, applicable to investigate first-order systems only, is no longer relevant. In this manuscript, a recently introduced methodology, generalizing the DRM technique to second-order systems, is applied to the models of Memristor CNN (M-CNN) cells, accomodating dynamic memristors. This allows to gain insights into the operating principles of these cellular structures, which make computations through the evolution of their states toward prescribed equilibria. Our analysis uncovers all possible local and global phenomena, which may emerge in the cell phase space under zero offset current for any self-feedback synaptic weight. Under these hypotheses, the dynamics of the M-CNN cell may significantly differ from those of a standard space-invariant CNN counterpart. The insertion of an offset current into each cell endows it with further properties, including monostability. The analysis method is used to demonstrate how a non-autonomous memristive array exploits the capability of its cells to feature monostability or bistability, depending upon the respective offset currents, to compute the element-wise logical AND between two binary images. [ABSTRACT FROM AUTHOR]