Inducing chaos in digital memcomputing machines via discrete-time integration

We numerically investigate the dynamics of digital memcomputing machines (DMMs), a class of nonlinear dynamical systems engineered to solve combinatorial optimization problems, and analyze how their problem-solving capabilities are influenced by the size of the integration time step. Specifically, we focus on the extreme limit of large time steps to minimize the number of integration steps required to reach a solution. By examining the system's phase space, calculating Lyapunov exponents, and analyzing power spectra, we reveal the conditions under which these systems transition to chaotic behavior. Our discussion highlights how discrete-time noise contributes to the onset of chaos, offering new insights into the performance and underlying dynamics of DMMs.