Edge of Chaos Theory Explains Complex Phenomena in Memristor Circuits

Edge of Chaos theory explains complex phenomena in memristor circuits design and unconventional computing. This slide book chapter discusses the complex necessary conditions of designing systems built with memristors. The generation of an action potential and solution of Chua's riddle is explained using the principle of Local Activity. The complex necessary conditions are stated by Erwin Schrodinger and Ilya Prigogine through external supply of energy and non-linearity. Amplifying infinitesimal fluctuations in energy create the local activity of a physical system. The local activity principle is explained in depth in the book chapter by Leon Chua, which lays the foundations of this discussion. The emergence of complex patterns in a homogeneous medium is well explained in the local activity principle. Using the theory of non-linear electronic circuits, nonlinear reaction-diffusion equations in physical systems were realized using a generic memristor model. A current-controlled locally passive memristor voltage-current characteristics and its state solutions for possible operating points are discussed. Generic memristor model of miniaturized volatile niobium oxide with locally active behavior and their experimental observations are discussed. The importance of Memristor Dynamic Route Map under current control and voltage control, NDR (Negative Differential Resistance) and PDR (Positive Differential Resistance) operating points on DC biasing circuits and its stabilization is explained. The chapter discusses the development of a systematic and rigorous approach to design bio-inspired circuits with the small-signal memristive amplifiers outlining the conditions for system complexity according to the theory of Local Activity and Edge of Chaos. The Edge of Chaos theory is interpreted as a new physics principle which extends the Second Law of Thermodynamics to open systems. The principle explains the hidden mechanisms underlying the emergence of Heterogeneous patterns in Homogeneous Media.