as a function of the properties of the physical memristive network and the external sources, where x i is the internal memory parameter of each device. The equation is valid in the case of the Strukov original toy model and it can be considered as a generalization of the single device model; in the case of ideal memristors, α α = 0 , although the hypothesis of the existence of an ideal memristor is debatable. In the equation above, α α is the "forgetting" time scale constant, typically associated to memory volatility, while χ χ = R off − − R on R off is the adimensional ratio between the resistance gap and off resistance value. S → → is the vector of the voltage sources in series to each junction. Instead, Ω Ω is a projection matrix in which the circuit enters directly, by projecting on the fundamental loops of the graph; such matrix enforces Kirchhoff's laws. Interestingly, the equation is valid for any network topology simply by changing the corresponding matrix Ω Ω . The constant β β has the dimension of a voltage and is associated to the properties of the memristor ; its physical origin is the charge mobility in the conductor. The diagonal matrix and vector X = diag ⁡ ⁡ ( X → → ) and x → → respectively, are instead the dynamical internal value of the memristive devices, with values between 0 and 1. This equation thus requires adding extra constraints on the memory values in order to be reliable, but can be used for instance to predict analytically the presence of instantonic transitions in memristive networks.