An Analytic Approach to Nonlinearity Analysis of Memristor

The nonlinearity characteristics of memristor have been widely employed in artificial intelligence. However, existing studies do not provide much attention to the analytic analysis of nonlinearity. This paper presents an analytic approach to the nonlinearity of memristor by analyzing the output spectrum based on homotopy analysis method (HAM). The analytic spectrum expressions obtained by this approach are verified by the fingerprints of memristor. It can be simultaneously revealed that one of the potential sources of the nonlinearity is the large variation of state variable. Furthermore, we propose a mapping method based on the obtained total harmonic distortion (THD) and a new parameter-threshold frequency ω
_C
to investigate the relationship between the memristor transition (i.e., the transition of the memristor between a nonlinear resistor and a linear resistor) and the frequency of input signal. Especially, analytic output spectrum, THD, and threshold frequency ω
_C
can be solved without complex mathematical operations and, thus, compared with traditional works, the complexity of the proposed approach is reduced.