CYBERNETICS AND PHYSICS, VOL. 8, NO. 3, 2019, 114–120 INTERMITTENCY INDUCED IN A BISTABLE MULTISCROLL ATTRACTOR BY MEANS OF STOCHASTIC MODULATION Jos´ e L. Echenaus´ ıa-Monroy Laboratory of Dynamical Systems CULagos, Universidad de Guadalajara M´ exico jose.echenausia@lagos.udg.mx Guillermo Huerta-Cuellar ∗ Laboratory of Dynamical Systems CULagos, Universidad de Guadalajara M´ exico ∗ Corresponding author: g.huerta@lagos.udg.mx Rider Jaimes-Re´ ategui Laboratory of Dynamical Systems CULagos, Universidad de Guadalajara, M´ exico rjaimes@culagos.udg.mx Juan H. Garc´ ıa-L´ opez Laboratory of Dynamical Systems CULagos, Universidad de Guadalajara, M´ exico hugog@culagos.udg.mx H´ ector E. Gilardi-Vel´ azquez Facultad de Ingenier´ ıa Universidad Panamericana M´ exico hectorgilardi@gmail.com Article history: Received 16.10.2019, Accepted 26.11.2019 Abstract In this work, numerical results of a nonlinear switch- ing system that presents bistable attractors subjected to stochastic modulation are shown. The system exhibits a dynamical modification of the bistable attractor, giving rise to an intermit behavior, which depends of modula- tion strength. The resulting attractor converge to an in- termittent double-scroll, for low amplitude modulation, and a 9-scroll attractor for a higher applied noise ampli- tude. A Detrended Fluctuation Analysis (DFA) applied to the x state variable, shows a perturbations robust- ness region, since the increase of noise does not present changes. Due to the applied noise, the final obtained system has higher randomness, compared with the orig- inal one. The understanding of the dynamical behavior of multiscrolls systems is highly important for advanc- ing technology in communications, as well in memory systems applications. Key words Multiscroll, Intermittency, Dynamics, Bistability. 1 Introduction In many nonlinear dynamical systems, intermittency is a common behavior, characterized by irregular burst that modify regular behavior [Manneville & Pomeau, 1979]. Different types of intermittency can be mentioned, e.g., type I and on-off intermittency are related with saddle- node bifurcations, type II and type III with Hopf and inverse period-doubling bifurcations, respectively, and crisis-induced intermittency with a crisis of chaotic at- tractors [Manneville & Pomeau, 1979; Hirsh, Nauen- berg, & Scalpino , 1982; Hirsh, Huberman, & Scalpino; Hu, & Rudnick]. For systems that show multistable be- havior, noise presence can be useful to influence inter- esting dynamics as hopping attractor [Kraut, & Feudel; Huerta-Cuellar et. al.; Pisarchik et. al.], as physical and natural phenomenons [Huerta-Cuellar et. al.; Pisarchik et. al; Gelens et. al.]. Also, noise can induce on-off inter- mittency in those systems that exhibit bistable behavior [Campos-Mejia, 2013]. A system with periodic poten- tial in the high frequency regime could shows the occur- rence of intermittency as the case of a pendulum, where the linear-response theory yields maximum frequency- dependent mobility as noise strength function [Saikia et al., 2011]. In the case of systems that generates intermittent ac- tivity, an analysis and characterization of the equilib- rium points number in a Chua multiscroll system by ap- plied noise was shown by [Arathi, Rajasekar, & Kurths]. In that sense, the generation of systems with scrolls in their phase space, such as the Lorenz and Chua systems [Lorenz, 1963; Chua, 1992], have been extensively stud- ied from a dynamical point of view, being the Lorenz at- tractor a particular case with intermittent behavior [Man- neville & Pomeau, 1979]. Over the past few years, the design and control of systems with multiple scrolls have been a subject of interest for the scientific com- munity [Echenaus´ ıa-Monroy, & Huerta-Cu´ ellar], hav-