Di Ventra Massimiliano, Traversa Fabio L
Department of Physics, University of California, San Diego, La Jolla, California 92093-0319, USA.
MemComputing, Inc., San Diego, California 92130, USA.
Chaos. 2017 Oct;27(10):101101. doi: 10.1063/1.5004431.
In Traversa and Di Ventra [Chaos 27, 023107 (2017)] we argued, without proof, that if the non-linear 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.
在特拉韦尔萨和迪文特拉的论文《混沌》第27卷，023107 (2017) 中，我们未经证明地提出，如果描述数字内存计算机（DMM）类别的具有记忆的非线性动力系统存在平衡点，那么就不会出现周期轨道。事实上，这一陈述的证明是特拉韦尔萨和迪文特拉在《混沌》第27卷，023107 (2017) 中已经证明的一个定理的简单推论。在此，我们指出如何得出这样的结论。顺便提一下，同样的论证意味着不存在混沌，这是我们已经在迪文特拉和特拉韦尔萨的论文《物理快报A》第381卷，3255 (2017) 中使用拓扑学证明的结果。这些结果，连同特拉韦尔萨和迪文特拉在《混沌》第27卷，023107 (2017) 中的结果，保证如果DMM设计用来解决的布尔问题有解，那么无论初始条件如何，系统总能找到它。
