Regularization of chaos by noise in electrically driven nanowire systems

Abstract

The electrically driven nanowire systems are of great importance to nanoscience and engineering. Due to strong nonlinearity, chaos can arise, but in many applications it is desirable to suppress chaos. The intrinsically high-dimensional nature of the system prevents application of the conventional method of controlling chaos. Remarkably, we find that the phenomenon of coherence resonance, which has been well documented but for low-dimensional chaotic systems, can occur in the nanowire system that mathematically is described by two coupled nonlinear partial differential equations, subject to periodic driving and noise. Especially, we find that, when the nanowire is in either the weakly chaotic or the extensively chaotic regime, an optimal level of noise can significantly enhance the regularity of the oscillations. This result is robust because it holds regardless of whether noise is white or colored, and of whether the stochastic drivings in the two independent directions transverse to the nanowire are correlated or independent of each other. Noise can thus regularize chaotic oscillations through the mechanism of coherence resonance in the nanowire system. More generally, we posit that noise can provide a practical way to harness chaos in nanoscale systems.

Control of tipping points in stochastic mutualistic complex networks

“…The unstable state between the basins of the survival state and the extinction state designates the basin boundary separating the two stable steady states. 43,[52][53][54][55][56][57] There are two possibilities for a system to achieve a transition between two steady states. The first is through a change in the system parameters within the system.…”

On the Chaotic Vibrations of Electrostatically Actuated Arch Micro/Nano Resonators: A Parametric Study

“…Park et al [2008] studied the chaotic response of a MEMS resonator and implemented a control strategy for the suppression of chaos, and consequently, performance enhancement. Hessari et al [2014] argued that electrically driven nanowires, subjected to an optimal level of white or colored noise, are capable of avoiding chaos and presenting more regular oscillations. Demartini et al [2007] implemented the Melnikov method to describe the chaotic region in parameter space of a micro-electro-mechanical oscillator.…”

Noise-enabled species recovery in the aftermath of a tipping point

“…The benefits of noise to nonlinear dynamical systems from the viewpoints of understanding certain natural phenomena and of engineering applications such as signal processing have been known and extensively studied since the discovery of the phenomenon of stochastic resonance [17][18][19][20][21][22][23] where, counterintuitively, a certain amount of deliberately applied noise can enhance and maximize the signal-to-noise ratio of the output of the system. A related phenomenon is noise-induced frequency [24] or coherence resonance [25][26][27][28] where noise can be exploited to improve, sometimes significantly, the temporal regularity of the output signal of a nonlinear oscillator by inducing or enhancing a dominant frequency component in its Fourier power spectrum. Ecological systems are fundamentally nonlinear [1][2][3], but the approach of purely deterministic modeling may not be sufficient to describe, characterize, and understand ecological phenomena in the real world due to the ubiquitous occurrence of various random forces in nature [4,6,10,11].…”

“…The concept of stochastic resonance was originally proposed [17] to explain the Quaternary glacial problem. Generally, it is a phenomenon in which the presence of internal or external noise in a nonlinear system can enhance the response of the system output [17][18][19][20][21][22][23][24][25][26][27][28]. The paradigmatic setting to demonstrate stochastic resonance is a bistable system, which occurs when a periodic force is applied in the presence of a large broadband random force (e.g., noise).…”