Edge of Chaos Clarifies the Origin for Yet-Unexplained Nonlinear Phenomena in Biological Systems

This pedagogical article introduces the simplest ever-reported bio-inspired circuit, which experiences symmetry-breaking instabilities under the effect of diffusion processes. Leveraging the capability of a NbO memristor to act as a local source of energy under suitable polarization, the proposed circuit reproduces the very same emerging phenomenon, known as destabilization of the homogeneous, first observed by Alan M. Turing in a two-cell array back in 1952, while employing half the number of degrees of freedom as compared to the original reaction-diffusion system discussed by the father of artificial intelligence. The proposed circuit is a two-cell memristor cellular neural network, which employs just two dynamic circuit elements, specifically two globally-passive yet locally-active volatile resistance switching memories, based upon niobium oxide and fabricated at NaMLab, besides three linear and passive resistors, and two DC voltage sources. A.M. Turing spent a huge amount of time to tune by trial and error the coefficients, appearing in the equations of the proposed fourth-order reaction-diffusion system, so as to demonstrate the emergence of dissipation-induced symmetry-breaking phenomena in a homogeneous cellular medium. On the other hand, the quantitative Theory of Local Activity, applicable universally to any physical system, allowed us to choose through a systematic methodology the circuit parameters of each of the two identical first-order memristive reaction cells so as to poise the composite second-order cell on the Edge of Chaos, which is the conditio sine qua non for the emergence of symmetry breaking phenomena, resulting in the steady-state formation of static patterns, across the bio-inspired system obtained after closing the composite cell itself across a suitable linear load resistance. In summary, together with the other contributions, such as the article published in the first edition of this book [asc21], the pedagogical work, presented here, sheds light into the necessity to recur to the Physics Principle of the Edge of Chaos to gain a deep understanding of the mechanisms underlying emergent phenomena in natural systems. [asc21] A. Ascoli, R. Tetzlaff, A.S. Demirkol, L.O. Chua, ''Edge of Chaos Theory Explains Complex Phenomena in Memristor Circuits,'' chapter in book entitled ''Selected Topics in Intelligent Chips with Emerging Devices, Circuits and Systems,'' River Publishers, Aalborg, Denmark, June 2023, e-ISBN: 9788770227643