Modeling of the generic memcapacitors using higher-order multi-ports

The paper introduces predictive modeling of generic memcapacitors using multi-port versions of fundamental elements of Chua’s table. Generic memcapacitors are the most common type of memcapacitive systems; they behave as state-dependent capacitors, with the capacitance being independent of the voltage and charge. The predictive model consists of a multiport capacitor and an associated dynamic system that represents the state of the dynamics. It is shown that the potential function of the multi-port is the energy of the electrostatic field of the memcapacitor. It enables incorporating this element into the framework of Lagrangian formalism. Practical implementations of the model are presented on specific examples from selected fields of science: a memory circuit with an electrostatically controlled bistable membrane, and a lipid bilayer model inspired by the processes that occur in cell membranes.