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Emergence of complex behavior in Memristor Cellular Nonlinear Networks (ECOM)

Subject Area Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
Term from 2017 to 2023
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 379950170
 
Final Report Year 2023

Final Report Abstract

We have investigated spatiotemporal pattern formation dynamics across a Reaction Diffusion Memristor Cellular Nonlinear Network (RD-MCNN) employing 3 different cell structures, each of which employ a locally active memristor being represented with physically meaningful models. The proposed resistively coupled RD-MCNN has a planar grid form and is composed of locally coupled identical cells. Focusing on the mathematical description of the memristors, we have investigated the HP NbOx device model and recast its equation set in a numerically efficient simplified generic form, which was utilized in the design of the first cell. Further simplifying the same generic form by the removal of the Mott box, we have obtained a broad generic locally active device model which is employed in the design of the second cell. Likewise, we have implemented a variable transformation in the Pickett model as a novel technique to improve its numerical stability and reduced the simulation time required. The resulting model was exploited in the design of the third cell. In order to facilitate further analytical calculations, we have derived a fruitful AC circuit equivalent for the locally active device models under investigation. The elements of the small signal equivalent were analytically expressed in terms model parameters for each DC operating point on the DC I-V loci. The derived AC circuit was used in the stability analysis of the three different single cell structures. We have performed comprehensive local activity and edge-of-chaos analysis both for the single devices and the isolated cell structures where the necessary conditions were expressed in an analytical form. Adopting the same approach, we have presented the destabilization analysis of the single cell qualitatively and, as a case study, the destabilization analysis of three coupled cells quantitatively. Thus, applying the theory of local activity, we have extracted the parameter space with locally active, edge-of-chaos, and sharp-edge-of-chaos domains, performing all the calculations parametrically. The corresponding parameter space domains are illustrated in terms of intrinsic network characteristics such as the cell DC operating point, the cell capacitance, and the coupling resistance. We have carried out extensive number of numerical simulations where we have demonstrated the emergence of pattern formation across the proposed RD-MCNN structure for various values of the design parameters. Dynamic pattern formation was studied through employing the 1st cell in a 2D RD-MCNN. In applications related to locomotion control, a RD-MCNN generating patterns with pronounced phase clustering may allow to synchronize the movements of the legs, whereas a structure supporting a wide range of spatiotemporal solutions may increase the memory capacity of an image recognition system. Static pattern formation was examined by employing the 2nd cell in the RD-MCNN. Various type of static patterns was observed, by including the effect of array size and the initially disturbed number of cells on the onset of simulations. We employed the 3rd cell in the RD-MCNN where we have focused on coupling through a nonlinear resistor which enhances the contrast and the dynamic range, and therefore, the visibility of the patterns, while creating new geometric features facilitating their classification. Moreover, we introduced a novel approach based upon the derivation of ternary pattern maps, where each pixel contains the information of the location of the static equilibria located on a specific region of the DC I m- Vm characteristic from a set of three possible branches. We conjecture that, in the future, these ternary pattern maps can also be employed for a fast detection and classification of emergent phenomena in MCNNs. The context of this project can be extended to the investigation of the impact of variability in parameter values and of the role of initial conditions on pattern formation. Following studies can focus on the development of strategies for the classification of the patterns generated and on the realization of the bio-inspired cellular arrays in hardware. It can be fruitful to investigate the impact of other kinds of nonlinearities for the constitutive relationships of the coupling resistor as well as of the bias resistor, which can introduce further control parameters to adjust the distribution of the DC equilibria of the cells' memristors along the DC Im-Vm curve. The analysis and design procedure introduced in parametric form for the investigation of pattern formation dynamics in MCNNs can be adopted to describe similar phenomena in arrays based upon other locally active resistance switching memories.

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