Steering multiattractors to overcome parameter inaccuracy and noise effects

Abstract

Steering of attractors in multistable systems is used to increase the available parameter domains which lead to stable dynamics in nonlinear physical systems, reducing substantially undesirable effects of parametric inaccuracy and noise. The procedure proposed here uses time and/or space asymmetric perturbations to move independent multistable attractors in phase space. Applying this mechanism we increase around 230% the stable domains in Hénon's map, roughly 85% in the ratchet current described by the Langevin equation and 60% in Chua's electronic circuit. The proposal is expected to have wide applications in generic nonlinear complex system presenting multistability, so that related experiments can increase robustness under parametric inaccuracy and noise.

Exploring an experimental analog Chua’s circuit

“…As another relevant contribution of the analog computation methodology presented in this work is to open possibilities to carry out experimental studies in nonlinear electronic circuits to verify the multistability phenomena, as reported in references [12][13][14]41], in the parameter planes of the Chua's circuit, as recently shown in a Chua's model [15,16], in which at least two stable periodic attractors coexist in the same set of control parameters but with different initial conditions. Besides, to perform experimental studies in the parameter planes of electronic circuits to corroborate the existence of the hidden attractors in these systems [17,18,42].…”

“…Even nowadays, significant results about these models are reported using numerical methods due to the advance of the modern computers and algorithms [7][8][9][10][11]. Specifically, we highlight the multistability phenomenon [12][13][14][15][16] and the hidden attractors [17,18] in the Chua circuits.…”

Optimal ratchet current for elastically interacting particles

“…However, when the value of coupling c between the maps RM (1) and RM (2) increases, optimal RCs can appear in distinct regions of the parameter space, differently from the case with one uncoupled particle in which high values of RCs are found only inside the ISSs. Finally, the duplication of the ISSs caused by the interacting ratchet (observed using external forces in 1-and 2-dimensional maps [21,25,26] and in continuous-time dynamical systems [27]) is a very interesting results and leads to an intriguing question regarding the dynamics of many particles interacting systems. It is possible to observe multiplication of ISSs when multiple ratchet are weakly coupled?…”

“…This methodology was successfully applied in the RM to retain thermal effects and to increase the area of the parameter space that leads to optimal RCs [21]. In the case of continuous systems, new stable attractors are not created but the steering of the existing multiple attractors in phase space was used to increase the regular region of the parameter space for the Langevin equation and for the Chua's electronic circuit [27]. This results lead us to conclude that duplications of stable regimes are closely related to multistability.…”

Coupling-induced periodic windows in networked discrete-time systems

“…The system exhibits duplication, triplication, and quadruplication of periodic windows when the perturbation is of periods two, three, and four, respectively [32]. Later on, the same phenomenon has been proposed as a mechanism to increase the availability of stable domains and, consequently, reduce the effects of noise and parameter inaccuracies in dynamical systems [33]. Moreover, replication of periodic windows has been recently shown to occur in a model for two asymmetrically coupled neurons [34].…”