Second order mem-circuits

This paper presents a comprehensive taxonomy of so-called second order memory devices, which include charge-controlled memcapacitors and flux-controlled meminductors, among other novel circuit elements. These devices, which are classified according to their differential and state orders, are necessary to get a complete extension of the family of classical nonlinear circuit elements (resistors, capacitors, inductors) for all possible controlling variables. Using a fully nonlinear formalism, we obtain nondegeneracy conditions for a broad class of second order mem-circuits. This class of circuits is expected to yield a rich dynamic behavior; in this regard we explore certain bifurcation phenomena exhibited by a family of circuits including a charge-controlled memcapacitor and a flux-controlled meminductor, providing some directions for future research

Are There an Infinite Number of Passive Circuit Elements in the World?

We found that a second-order ideal memristor [whose state is the charge, i.e., x=q in v=R(x,i,t)i] degenerates into a negative nonlinear resistor with an internal power source. After extending analytically and geographically the above local activity (experimentally verified by the two active higher-integral-order memristors extracted from the famous Hodgkin–Huxley circuit) to other higher-order circuit elements, we concluded that all higher-order passive memory circuit elements do not exist in nature and that the periodic table of the two-terminal passive ideal circuit elements can be dramatically reduced to a reduced table comprising only six passive elements: a resistor, inductor, capacitor, memristor, mem-inductor, and mem-capacitor. Such a bounded table answered an open question asked by Chua 40 years ago: Are there an infinite number of passive circuit elements in the world

Utilization of Euler-Lagrange Equations in Circuits with Memory Elements

It is well known that the equation of motion of a system can be set up using the Lagrangian and the dissipation function, which describe the conservative and dissipative parts of the system. However, this procedure, consisting in a systematic differentiation of the above state functions, cannot be used for circuits containing simultaneously conventional nonlinear elements such as the resistor, capacitor, and inductor, and their nonlinear memory versions – the memristor, memcapacitor, and meminductor. The paper provides a general solution to this problem and demonstrates it on the example of modeling Josephson’s junction

Beyond Memristors: Neuromorphic Computing Using Meminductors

Resistors with memory (memristors), inductors with memory (meminductors) and capacitors with memory (memcapacitors) play different roles in novel computing architectures. We found that a coil with a magnetic core is an inductor with memory (meminductor) in terms of its inductance L(q) being a function of charge q. The history of the current passing through the coil is remembered by the magnetization inside the magnetic core. Such a meminductor can play a unique role (that cannot be played by a memristor) in neuromorphic computing, deep learning and brain-inspired computers since the time constant of a neuromorphic RLC circuit is jointly determined by the inductance L and capacitance C, rather than the resistance R. As an experimental verification, this newly invented meminductor was used to reproduce the observed biological behavior of amoebae (the memorizing, timing and anticipating mechanisms). In conclusion, a beyond-memristor computing paradigm is theoretically sensible and experimentally practical