Existence of multiple operating points in memristive circuits

The asymptotic behavior of the memristor at dc yields a nonlinear i-u branch relationship, i.e. the memristor equivalent at dc is a nonlinear resistor. In this way, the resulting equilibrium equation of memristive circuits in dc regime has the form of system of nonlinear algebraic equations, which may have one solution, multiple solutions or no solution at all. In this work, the phenomenon of multiple dc operating points (MOPs) in memristor circuits is studied and the conditions for the occurrence of MOPs in a simple two-memristor circuit are established. Besides, homotopy methods are applied in order to find them.