Suppressing chaos in a simplest autonomous memristor-based circuit of fractional order by periodic impulses

In this paper, the chaotic behavior of a simplest autonomous memristor-based circuit of fractional order is suppressed by periodic impulses applied to one or several state variables. The circuit consists of two passive linear elements, a capacitor and an inductor, as well as a nonlinear memristive element. It is shown that by applying a sequence of adequate (identical or different) periodic impulses to one or several variables, the chaotic behavior can be suppressed. Impulse values and control timing are determined numerically, based on the bifurcation diagram with impulses as bifurcation parameters. Empirically, the probability to have a reasonably wide range of impulses to suppress chaos is quite large, ensuring that chaos suppression can be implemented, as demonstrated by several examples presented.