where X is the diagonal matrix with elements x i on the diagonal, α α , β β , χ χ are based on the memristors physical parameters. The vector S → → is the vector of voltage generators in series to the memristors. The circuit topology enters only in the projector operator Ω Ω 2 = Ω Ω , defined in terms of the cycle matrix of the graph. The equation provides a concise mathematical description of the interactions due to Kirchhoff 's laws. Interestingly, the equation shares many properties in common with a Hopfield network, such as the existence of Lyapunov functions and classical tunnelling phenomena. In the context of memristive networks, the CTD equation may be used to predict the behavior of memristive devices under different operating conditions, or to design and optimize memristive circuits for specific applications.