MEMRISTOR MODELS IN A CHAOTIC NEURAL CIRCUIT

Abstract

The peculiar features of the memristor, a fundamental passive two-terminal element characterized by a nonlinear relationship between charge and flux, promise to revolutionize integrated circuit design in the next few decades. Besides its most popular potential application, ultra-dense nonvolatile memories, much research has been lately devoted to their use in chaotic neural networks for the emulation of brain activity. In the studies on neuromorphic circuits, it is common to characterize each memristor with a theoretical model based upon a single-valued odd-symmetric charge-flux nonlinearity. Memristive nano-films exhibit different dynamics depending on the way they behave at boundaries. We recently developed a mathematical model, applicable to memristive nano-structures of various nature, offering the opportunity to tune the boundary conditions so as to capture a wide gamut of distinct nonlinear behaviors. However, in general the proposed model exhibits a multivalued charge-flux nonlinearity dependent on input and initial state condition. In this paper, we first derive the necessary and sufficient set of boundary conditions under which single-valuedness is observed in this nonlinearity for any input/state initial condition combination. Then, after proving that, under such boundary conditions, the asymmetrical nonlinearities of memristors with opposite orientation are the odd-symmetric function of the other, we devise a pair of suitable memristor arrangements with odd-symmetric charge-flux characteristics. This analysis is confirmed by showing how a chaotic neural circuit employing one of such arrangements behaves similarly to its counterpart with the theoretically-modeled memristor.