Memristor model based on fuzzy window function

Abstract

Abstract-Memristor (memory-resistor) is the fourth passive circuit element. We introduce a memristor model based on a fuzzy logic window function. Fuzzy models are flexible, which enables the capture of the pinched hysteresis behavior of the memristor. The introduced fuzzy model avoids common problems associated with window-function based memristor models, such as the terminal state problem, and the symmetry issues. The model captures the memristor behavior with a simple rule-base which gives an insight of how memristors work. Because of the flexibility offered by the fuzzy system, shape and distribution of input and output membership functions can be tuned to capture the behavior of various real memristors.

Importance of the Window Function Choice for the Predictive Modelling of Memristors

“…[4], [6], [11] satisfy the conditions of Theorem 1, the window functions introduced in Refs. [1], [2], [3], [5], [7], [8], [9], [10], [12] belong to the class covered by Theorem 2. Moreover, it should be stressed that the experimental identification of stable fixed points could be employed to refine the models used to describe a specific type/realization of memristor.…”

“…This subsection briefly introduces the window functions used in the present paper. As was mentioned above, window functions [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12] are frequent components of memristor models [6], [15]. Typically, their role is to slow down the change of x when the internal state variable x approaches a boundary value (such as 0 or 1).…”

“…To verify that x a is a stable fixed point, we substitute Eq. ( 12) into (10) and divide it by Eq. ( 13).…”

“…During the past decade there have been many publications using window function-based models [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12] to describe the response of either discrete memristors or their circuits. While in many cases such models provided reliable predictions, there are situations when the behavior of the circuit depends critically on the choice of window function.…”

Fuzzy Membership Function Implementation with Memristor

“…where D is full length of memristor, R on is the resistance when full length is doped and R of f is the resistance when total width of memristor becomes undoped , w 0 is the initial value of w, µ is the average ion mobility and q(t) is the amount of electric charge [14], [15]. The value of memristance depends on voltage and current applied to it.…”