Diversity-induced coherence resonance in spatially extended chaotic systems

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.

Double resonance induced by group coupling with quenched disorder

Results show that the astrocytes can not only listen to the talk of large assemble of neurons but also give advice to the conversations and are significant sources of heterogeneous couplings as well. In the present work, we focus on such regulation character of astrocytes and explore the role of heterogeneous couplings among interacted neuron-astrocyte components in a signal response. We consider reduced dynamics in which the listening and advising processes of astrocytes are mapped into the form of group coupling, where the couplings are normally distributed. In both globally coupled overdamped bistable oscillators and an excitable FitzHugh-Nagumo (FHN) neuron model, we numerically and analytically demonstrate that two types of bell-shaped collective response curves can be obtained as the ensemble coupling strength or the heterogeneity of group coupling rise, respectively, which can be seen as a new type of double resonance. Furthermore, through the bifurcation analysis, we verify that these resonant signal responses stem from the competition between dispersion and aggregation induced by heterogeneous group and positive pairwise couplings, respectively. Our results contribute to a better understanding of the signal propagation in coupled systems with quenched disorder.

Diversity-induced resonance in a globally coupled bistable system with diversely distributed heterogeneity

A moderate degree of diversity, in form of quenched noise or intrinsic heterogeneity, can significantly strengthen the collective response of coupled extended systems. As yet, related discoveries on diversity-induced resonance are mainly concentrated on symmetrically distributed heterogeneity, e.g., the Gaussian or uniform distributions with zero-mean. The necessary conditions that guarantee the arise of resonance phenomenon in heterogeneous oscillators remain largely unknown. In this work, we show that the standard deviation and the ratio of negative entities of a given distribution jointly modulate diversity-induced resonance and the concomitance of negative and positive entities is the prerequisite for this resonant behavior emerging in diverse symmetrical and asymmetrical distributions. Particularly, for a proper degree of diversity of a given distribution, the collective signal response behaves like a bell-shaped curve as the ratio of negative oscillator increases, which can be termed negative-oscillator-ratio induced resonance. Furthermore, we analytically reveal that the ratio of negative oscillators plays a gating role in the resonance phenomenon on the basis of a reduced equation. Finally, we examine the robustness of these results in globally coupled bistable elements with asymmetrical potential functions. Our results suggest that the phenomenon of diversity-induced resonance can arise in arbitrarily distributed heterogeneous bistable oscillators by regulating the ratio of negative entities appropriately.

Signal amplification enhanced by large phase disorder in coupled bistable units

We study the maximum response of network-coupled bistable units to subthreshold signals focusing on the effect of phase disorder. We find that for signals with large levels of phase disorder, the network exhibits an enhanced response for intermediate coupling strength, while generating a damped response for low levels of phase disorder. We observe that the large phase-disorder-enhanced response depends mainly on the signal intensity but not on the signal frequency or the network topology. We show that a zero average activity of the units caused by large phase disorder plays a key role in the enhancement of the maximum response. With a detailed analysis, we demonstrate that large phase disorder can suppress the synchronization of the units, leading to the observed resonancelike response. Finally, we examine the robustness of this phenomenon to the unit bistability, the initial phase distribution, and various signal waveform. Our result demonstrates a potential benefit of phase disorder on signal amplification in complex systems.

Anormal diffusion enhancement of resonant responses for coupled oscillator networks to weak signals

The normal diffusion effect is introduced as a new regulating factor into the established diffusive coupling model for bistable oscillator networks. We find that the response of the system to the weak signal is substantially enhanced by the anormal diffusion, which is termed anormal-diffusion-induced resonance. We also reveal that the diffusive coupling-induced transition, which changes the system from a bistable to a monostable state, is of fundamental importance for the occurrence of resonance. The proposed approach is validated using simulation studies and theoretical analyses. Our results suggest that diffusion induced resonance can be more easily observed in nonlinear oscillator networks.

Self-organization in a diversity induced thermodynamics

In this work we show how global self-organized patterns can come out of a disordered ensemble of point oscillators, as a result of a deterministic, and not of a random, cooperative process. The resulting system dynamics has many characteristics of classical thermodynamics. To this end, a modified Kuramoto model is introduced, by including Euclidean degrees of freedom and particle polarity. The standard deviation of the frequency distribution is the disorder parameter, diversity, acting as temperature, which is both a source of motion and of disorder. For zero and low diversity, robust static phase-synchronized patterns (crystals) appear, and the problem reverts to a generic dissipative many-body problem. From small to moderate diversity crystals display vibrations followed by structure disintegration in a competition of smaller dynamic patterns, internally synchronized, each of which is capable to manage its internal diversity. In this process a huge variety of self-organized dynamic shapes is formed. Such patterns can be seen again as (more complex) oscillators, where the same description can be applied in turn, renormalizing the problem to a bigger scale, opening the possibility of pattern evolution. The interaction functions are kept local because our idea is to build a system able to produce global patterns when its constituents only interact at the bond scale. By further increasing the oscillator diversity, the dynamics becomes erratic, dynamic patterns show short lifetime, and finally disappear for high diversity. Results are neither qualitatively dependent on the specific choice of the interaction functions nor on the shape of the probability function assumed for the frequencies. The system shows a phase transition and a critical behaviour for a specific value of diversity.

The study of amplitude death in globally delay-coupled nonidentical systems based on order parameter expansion

The method of order parameter expansion is used to study the dynamical behavior in the globally delay-coupled nonidentical systems. Using the Landau-Stuart periodic system and Rössler chaotic oscillator to construct representative systems, the method can identify the boundary curves of amplitude death island analytically in the parameter space of the coupling and time delay. Furthermore, the parameter mismatch (diversity) effect on the size of island is investigated numerically. For the case of coupled chaotic Rössler systems with different timescales, the diversity increases the domain of death island monotonically. However, for the case of delay-coupled Landua-Stuart periodic systems with different frequencies, the average frequency turns out to be a critical role that determines change of size with the increase of diversity.

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.