Stochastic Implementation and Analysis of Dynamical Systems Similar to the Logistic Map

Abstract

Stochastic computing (SC) is a digital computation approach that operates on random bit streams to perform complex tasks with much smaller hardware footprints compared with conventional binary radix approaches. SC works based on the assumption that input bit streams are independent random sequences of 1s and 0s. Previous SC efforts have avoided implementing functions that have feedback, because doing so has the potential for creating highly correlated inputs. We propose a number of solutions to overcome the challenges of implementing feedback in stochastic logic. We use a family of dynamical system functions that are similar to the well-known logistic map $x \to \mu x(1-x)$ as case studies. We show that complex behaviors, such as period doubling and chaos, do indeed occur in digital logic with only a few gates operating on a few 0s and 1s. Our energy consumption is between 21% and 31% of the conventional binary approach. In order to verify our design methodology, we have measured the mean switching rate between the basins of attraction of two coexisting fixed points and the peak width of the steady-state distribution of the output using a logistic-map-like function as an example. Theoretical results match well with our numerical experiments.