Absence of periodic orbits in digital memcomputing machines with solutions

作者：Di Ventra Massimiliano^*; Traversa Fabio L

来源：Chaos, 2017, 27(10): 101101.

DOI：10.1063/1.5004431

In Traversa and Di Ventra [Chaos 27, 023107 (2017)] we argued, without proof, that if the nonlinear dynamical systems with memory describing the class of digital memcomputing machines (DMMs) have equilibrium points, then no periodic orbits can emerge. In fact, the proof of such a statement is a simple corollary of a theorem already demonstrated in Traversa and Di Ventra [Chaos 27, 023107 (2017)]. Here, we point out how to derive such a conclusion. Incidentally, the same demonstration implies absence of chaos, a result we have already demonstrated in Di Ventra and Traversa [Phys. Lett. A 381, 3255 (2017)] using topology. These results, together with those in Traversa and Di Ventra [Chaos 27, 023107 (2017)], guarantee that if the Boolean problem the DMMs are designed to solve has a solution, the system will always find it, irrespective of the initial conditions. Published by AIP Publishing.

• 出版日期2017-10