The tractability index of memristive circuits: branch-oriented and tree-based models

The memory-resistor or memristor is a new electrical element characterized by a nonlinear charge-flux relation. This device poses many challenging problems, in particular from the circuit modeling point of view. In this paper we address the index analysis of certain differential-algebraic models of memristive circuits; specifically, our attention is focused on so-called branch-oriented models, which include in particular tree-based formulations of the circuit equations. Our approach combines results coming from DAE theory, matrix analysis and the theory of digraphs. This framework should be useful in future studies of dynamical aspects of memristive circuits