Spatially correlated diversity-induced resonance

Nonmonotonic enhancement of diversity-induced resonance in systems of mobile oscillators

Diversity is omnipresent in natural and synthetic extended systems, the phenomenon of diversity-induced resonance (DIR), wherein a moderate degree of the diversity can provoke an optimal collective response, provides researchers a brand-new strategy to amplify and utilize the weak signal. As yet the relevant advances focus mostly on the ideal situations where the interactions among elements are uncorrelated with the physical proximity of agents. Such a consideration overlooks interactions mediated by the motion of agents in space. Here, we investigate the signal response of an ensemble of spatial mobile heterogeneous bistable oscillators with two canonical interacting modes: dynamic and preset. The oscillators are considered as mass points and perform random walks in a two-dimensional square plane. Under the dynamic scheme, the oscillators can only interact with other oscillators within a fixed vision radius. For the preset circumstance, the interaction among oscillators occurs only when all of them are in a predefined region at the same moment. We find that the DIR can be obtained in both situations. Additionally, the strength of resonance nonmonotonically rises with respect to the increase of moving speed, and the optimal resonance is acquired by an intermediate magnitude of speed. Finally, we propose reduced equations to guarantee the occurrence of such mobility-optimized DIR on the basis of the fast switching approximation theory and also examine the robustness of such phenomenon through the excitable FitzHugh-Nagumo model and a different spatial motion mechanism. Our results reveal for the first time that the DIR can be optimized by the spatial mobility and thus has promising potential application in the communication of mobile agents.

Effects of phase disorder on transport of globally coupled Brownian motors

The transport of N globally coupled Brownian motors driven by a periodic force with phase disorder is investigated. An approximate theoretical analysis of the model is presented. The effects of the phase disorder and the driving strength of the periodic force on the transport of the coupled Brownian motors are discussed both theoretically and numerically. It is found that the increase of the periodical driving force decreases the average velocity, while the coupled particles may benefit from the phase disorder to enhance collective transport.

Delay and diversity-induced synchronization transitions in a small-world neuronal network

The synchronized behaviors of a noisy small-world neuronal network with delay and diversity is numerically studied by calculating a synchronization measure and plotting firing pattern. We show that delay in the information transmission can induce fruitful synchronization transitions, including transition from phase locking to antiphase synchronization, and transition from antiphase synchronization to complete synchronization. Furthermore, the delay-induced complete synchronization can be changed by diversity, which causes the oscillatory-like transition between antiphase synchronization and complete synchronization.

Diversity-induced resonance on weighted scale-free networks

The diversity-induced resonance in weighted scale-free networks is investigated numerically and analytically. The couplings are weighted according to node degree. It is found that self-organized phase shifts occur between large-degree and small-degree nodes, although there is no time delay in coupling terms. Such spontaneous phase shifts are relevant to the improvement of signal resonance amplification. This finding may help to better understand how the collective behavior of individual units promotes the response of the whole system to external signals.

Effects of clustering on diversity-induced resonance in hidden metric spaces

The effects of network clustering on diversity-induced resonance of an ensemble of bistable systems subjected to weak signals are investigated. A class of network models based on hidden metric spaces is used to generate networks with different levels of clustering. The propensity of triples of nodes is to form triangles. By numerical simulations and analytical calculations, it is shown that the maximum response is suppressed by network clustering. The optimal diversity strength for maximum response is also reduced. A pronounced resonance phenomenon is observed at an intermediate clustering strength. Either low or high clustering strength will undermine the response of the systems to external signals. The results imply that it is possible to control the response of spatially extended systems to external signals by the manipulation of network clustering.