  Memristor has great application prospects in various high-performance
electronic systems, such as memory, artificial intelligence, and neural
networks, due to its fast speed, nano-scale dimensions, and low-power
consumption. However, traditional nonanalytic models and lately reported
analytic models for memristor have the problems of nonconvergence and slow
convergence, respectively. These problems lay great obstacles in the analysis,
simulation and design of memristor. To address these problems, a modeling
methodology for analytic approximate solution of the state variable in
memristor is proposed in this work. This methodology solves the governing
equation of memristor by adopting the Homotopy Analysis Method (HAM) for the
first time, and the convergence performance of the methodology is enhanced by
an optimized convergence-control parameter in the HAM. The simulation results,
compared with the reported analytic models, demonstrate that the HAM-based
modeling methodology achieves faster convergence while guaranteeing sufficient
accuracy. Based on the methodology, it can be simultaneously revealed that
highly nonlinearity is the potential sources of slow convergence in analytic
models, which is beneficial for the analysis and design guidance. In addition,
a Spice subcircuit is constructed based on the obtained HAM model, and then it
is integrated into an oscillator to verify its applicability. Due to the
generality of HAM, this methodology may be easily extended to other memory
devices.
