Bichaoticity induced by inherent birhythmicity during the oscillatory electrodissolution of silicon

Abstract

The electrodissolution of p-type silicon in a fluoride-containing electrolyte is a prominent electrochemical oscillator with a still unknown oscillation mechanism. In this article, we present a study of its dynamical states occurring in a wide range of the applied voltage–external resistance parameter plane. We provide evidence that the system possesses inherent birhythmicity, and thus at least two distinct feedback loops promoting oscillatory behavior. The two parameter regions in which the different limit cycles exist are separated by a band in which the dynamics exhibit bistability between two branches with different multimode oscillations. Following the states along one path through this bistable region, one observes that each branch undergoes a different transition to chaos, namely, a period doubling cascade and a quasiperiodic route with a torus-breakdown, respectively, making Si electrodissolution one of the few experimental systems exhibiting bichaoticity.

Multi-synchronization and other patterns of multi-rhythmicity in oscillatory biological systems

“…The coexistence between two rhythmic patterns of electrical activity has also been found theoretically in studies of periodically stimulated cardiac cells [35–37] and in models of nerve cells regulated through mutual inhibition [38–40]. Besides these theoretical studies, experimental evidence for birhythmicity has been obtained in some chemical oscillatory systems [41,42] and also in a number of biological examples ranging from periodically stimulated cardiac cells [36,37] to nerve cells [43–45], the production of different registers of human voice [46,47], and an ecological system [48,49].…”

“…The coexistence of multiple rhythms appears to be less widespread than the coexistence of multiple steady states. Some chemical examples of birhythmicity have been reported experimentally [41,42]. In biological systems, birhythmicity was demonstrated experimentally and theoretically in periodically stimulated cardiac cells, in which two patterns of entrainment may coexist [36,37].…”

Nonlinear Chemical Dynamics and Its Interdisciplinary Impact: Dedicated to Ken Showalter on the Occasion of his 70th Birthday

“…An electrochemical phenomenon is also the focus in the work by Tosolini et al, 32 who investigated the electrodissolution of p-type silicon. The authors describe birhythmicity in this system, which indicates the existence of at least two distinct feedback loops.…”

Stochastic transformations of multi-rhythmic dynamics and order–chaos transitions in a discrete 2D model

“…Many real systems are characterized by birhythmicity with the coexistence of two periodic attractors, both regular and chaotic (see, e.g., Refs. [34][35][36]. A problem of the switching between multiple periodic attractors was studied in Refs.…”