In this paper, we show that a voltage-controlled nonlinear resistor can be regarded as a voltage-controlled memristor when its behavior is observed using the time derivatives of state variables. Next, we derive the memristor FitzHugh-Nagumo equation by differentiating the original FitzHgh-Nagumo equation with respect to time. We also show that the trajectory of the memristor FitzHugh-Nagumo equation is highly dependent on the initial flux condition. This trajectory can be changed by applying a small single pulse. Furthermore, the square wave forcing creates many complex behaviors such as chaotic attractors and limit cycles. These behaviors also depend on the initial flux condition. Therefore, it is impossible to predict the trajectory without knowing the initial flux condition. Next, we observe the trajectory's evolution by adding a small DC bias current to the square wave forcing. We show that as time progresses, the trajectory changes shape and eventually shrinks. This resembles the refractory period of neurons. Finally, we study the signal transmission between the two memristor FitzHugh-Nagumo circuits which are connected by a unity-gain buffer. We show that, for the signal to be transmitted almost exactly, the initial flux condition must be identical. Additionally, we derive the memristor Chua circuit equation by differentiating the original Chua circuit equation with respect to time. Our findings are nearly identical to those for the memristor FitzHugh-Nagumo equation. We also study the signal transmission between two memristor Chua circuits that are connected by a unity-gain buffer. We show that nearly perfect transmission requires the identical initial flux condition. It should be noted that requiring the identical initial flux conditions results in more secure communication with the memristor Chua circuits than with the original Chua circuits. Finally, we would like to emphasize the following points: The memristor FitzHugh-Nagumo equation and the memristor Chua circuit equation both exhibit rich dynamics. The identification of the circuit elements depends on the coordinate system used to observe them.