Model dependency of memristor circuit dynamics

Pickett's model is one of the few memristor models based upon experimental observations. Despite its high degree of accuracy, it is fairly complex and its use in large circuits is problematic. A number of simpler memristor models, specifically Biolek's model, the generalized Boundary Condition Memristor model and the ThrEshold Adaptive Memristor model are capable to track the dynamics of Pickett's model after undergoing a proper optimization process. However, since the parameter values of Pickett's model need to be tuned on the basis of the way the memristor is coupled to other circuit components including the input source, the optimization procedure is not unique but must be repeated on a case by case basis. This is non ideal since the parameters of Pickett's model were only given for a few circuit/input scenarios. Further, employing these models in simple memristor-based circuits without a preliminary necessary optimization step, simulations results reveal the occurrence of distinct nonlinear behaviors under a common setting for the circuit components coupled to the memristor. These issues demonstrate that the current lack of a finalized model for the physical memristor prevents memristorbased electronics to flourish. Preliminary investigations on a novel polynomial model show that Prof. Chua's idea of ''unfolding the memristor'' by suitably expanding the morphing function in series of polynomials involving state and input could represent the key towards the ultimate model.