Critical role of initial condition in the dynamics of memristive systems: Orbital narrowing revisited

This paper explores the characterization of memristive systems utilizing the characteristive curve of state and analyze the special role of initial condition in such history-dependent systems. The specifically studied system focuses on the titanium dioxide memristor based on the nonlinear ionic drift model of Joglekar. We derive first the characteristic curve of state (CCOS) as the analytical solution of the model to any integer index in the Gaussian hypergeometric form, based on which a characterization approach is then developed. The approach simply converts the complicated history-dependent dynamics into a mapping on the state-flux phase plane, expressing the initial condition as a pure translation along the flux axis, which is analogous to the characterization method for transistors. With this geometric view, we observe that the initial condition operates as an operation point for a memristive system and can effectively influence the orbital shape: the same input signal can produce two distinct orbital shapes when the initial conditions differ. From another point, there ought to be two factors giving rise to the orbital narrowing phenomenon: the frequency and the initial condition. It is pointed out that this is purely caused by the nonlinearity in the model.