Phase coherence and attractor geometry of chaotic electrochemical oscillators

Abstract

Chaotic attractors are known to often exhibit not only complex dynamics but also a complex geometry in phase space. In this work, we provide a detailed characterization of chaotic electrochemical oscillations obtained experimentally as well as numerically from a corresponding mathematical model. Power spectral density and recurrence time distributions reveal a considerable increase of dynamic complexity with increasing temperature of the system, resulting in a larger relative spread of the attractor in phase space. By allowing for feasible coordinate transformations, we demonstrate that the system, however, remains phase-coherent over the whole considered parameter range. This finding motivates a critical review of existing definitions of phase coherence that are exclusively based on dynamical characteristics and are thus potentially sensitive to projection effects in phase space. In contrast, referring to the attractor geometry, the gradual changes in some fundamental properties of the system commonly related to its phase coherence can be alternatively studied from a purely structural point of view. As a prospective example for a corresponding framework, recurrence network analysis widely avoids undesired projection effects that otherwise can lead to ambiguous results of some existing approaches to studying phase coherence. Our corresponding results demonstrate that since temperature increase induces more complex chaotic chemical reactions, the recurrence network properties describing attractor geometry also change gradually: the bimodality of the distribution of local clustering coefficients due to the attractor’s band structure disappears, and the corresponding asymmetry of the distribution as well as the average path length increase.

Signatures of chaotic and stochastic dynamics uncovered with ε -recurrence networks

“…Similar observations were made for the network measures L and R (electronic supplementary material, figures S2 and S3). From figure 5, it can be seen that L distinguishes between hyper-chaotic and stochastic dynamics quite well for increasing m. As N is increased, L for the hyper-chaotic system begins to decrease as the spread of the attractor increases in the phase space (hyper-chaos is better characterized geometrically with increasing data length) and this creates shortcuts between distant attractor points [60]. Also, in the case of network measures D T and R (figure 5), the distinction between hyper-chaotic and stochastic dynamics improved with increasing N and m. These results are expected as a higher number of data points leads to a better characterization of the underlying hyper-chaotic dynamics.…”

Characterizing system dynamics with a weighted and directed network constructed from time series data

“…The chaotic dynamics we consider here are simply the archetypal chaotic R€ ossler system. Differences in results between phase coherent and funnel regime dynamics, for example, 34 may also provide significant results. As shown in Fig.…”

Visibility graph analysis for re-sampled time series from auto-regressive stochastic processes

“…For example, recurrence network approaches have been applied to climate data analysis [4,7] , chaotic electro-chemical oscillators [8] , or two-phase flow data [9] . Some basic network motif structures have be identified in music data [10] .…”