Positive and negative couplings perform complementary roles in the signal amplification of globally coupled bistable oscillators

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.

Influence of inhibitory autapses on synchronization of inhibitory network gamma oscillations

A recent experimental study showed that inhibitory autapses favor firing synchronization of parvalbumin interneurons in the neocortex during gamma oscillations. In the present paper, to provide a comprehensive and deep understanding to the experimental observation, the influence of inhibitory autapses on synchronization of interneuronal network gamma oscillations is theoretically investigated. Weak, middle, and strong synchronizations of a globally inhibitory coupled network composed of Wang-Buzsáki model without autapses appear at the bottom-left, middle, and top-right of the parameter plane with the conductance (gsyn) and the decay constant (τsyn) of inhibitory synapses taken as the x-axis and y-axis, respectively. After introducing inhibitory autapses, the border between the strong and middle synchronizations in the (gsyn, τsyn) plane moves to the top-right with increasing the conductance (gaut) and the decay constant (τaut) of autapses, due to that interspike interval of the single neuron becomes longer, leading to that larger τsyn is needed to ensure the strong synchronization. Then, the synchronization degree of middle and strong synchronizations around the border in the (gsyn, τsyn) plane decreases, while of strong synchronization in the remaining region remains unchanged. The synchronization degree of weak synchronization increases with increasing τaut and gaut, due to that the inhibitory autaptic current becomes strong and long to facilitate synchronization. The enhancement of weak synchronization modulated by inhibitory autapses is also simulated in the random, small-world, and scale-free networks, which may provide explanations to the experimental observation. These results present complex dynamics of synchronization modulated by inhibitory autapses, which needs future experimental demonstrations.

Enhanced signal response in globally coupled networks of bistable oscillators: Effects of mean field density and signal shape

This paper studies a set of globally coupled bistable oscillators, all subjected to the same weak periodic signal and identical coupling. The effect of mean field density (MFD) on global dynamics is analyzed. The oscillators switch from intra- to interwell motion as MFD increases, clearly demonstrating MFD-enhanced signal amplification. A maximum amplification also occurs at a moderate level of MFD, indicating that the response exhibits a nonmonotonic sensitivity to MFD. The MFD-enhanced response depends mainly on the signal intensity but not on the signal frequency or the network topology. The analytical investigation provides a simplified model to study the mechanism underlying this resonancelike behavior. It is shown that by modifying the bistability nature of the potential energy, the mean field density can promote well-to-well oscillations and larger amplitude motions. Finally, the robustness of this phenomenon to various signal waveforms is examined. It can therefore be used alternatively to efficiently amplify weak signals in practical situations with large network sizes.

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.

Heterogeneity induced splay state of amplitude envelope in globally coupled oscillators

Splay states of the amplitude envelope are stably observed as a heterogenous node is introduced into the globally coupled identical oscillators with repulsive coupling. With the increment of the frequency mismatches between the heterogenous nodes and the rest identical globally coupled oscillators, the formal stable splay state based on the time series becomes unstable, while a splay state based on the new-born amplitude envelopes of time series is stably observed among the rest identical oscillators. The characteristics of the splay state based on the amplitude envelope are numerically and theoretically presented for different parameters of the coupling strength ϵ and the frequency mismatches Δω for small coupling strength and large frequency mismatches. We expect that all these results could reveal the generality of splay states in coupled nonidentical oscillators and help to understand the rich dynamics of amplitude envelopes in multidisciplinary fields.

Amplified signal response by cluster synchronization competition in rings with short-distance couplings

Topological resonance has been revealed in degree-heterogeneous scale-free networks for weak signal amplification, but not in degree-homogeneous all-to-all networks [Acebrón et al., Phys. Rev. Lett. 99, 128701 (2007)0031-900710.1103/PhysRevLett.99.128701]. Here, we show that when the coupling distance of the all-to-all networks is reduced from global to local, i.e., converting all-to-all networks into rings, we can observe a resonant response to a weak signal similar to scale-free networks. We find that such a resonance effect induced by ring topology is robust across a wide range of ring sizes and signal frequencies. We further show that at intermediate coupling strength, oscillators in the rings can form separate synchronous clusters that compete with each other, resulting in large amplitude oscillations of boundary nodes between clusters and thus giving rise to the resonant signal amplification. Finally, we propose a structure of a three-node feed-forward motif simplified from the observed cluster synchronization competition to analyze the mechanism underlying the resonance behavior, which corresponds well with the numerical results.

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.

Diversity-induced resonance for optimally suprathreshold signals

Recent research has revealed that a system of coupled units with a certain degree of parameter diversity can generate an enhanced response to a subthreshold signal compared to that without diversity, exhibiting a diversity-induced resonance. We here show that diversity-induced resonance can also respond to a suprathreshold signal in a system of globally coupled bistable oscillators or excitable neurons, when the signal amplitude is in an optimal range close to the threshold amplitude. We find that such diversity-induced resonance for optimally suprathreshold signals is sensitive to the signal period for the system of coupled excitable neurons, but not for the coupled bistable oscillators. Moreover, we show that the resonance phenomenon is robust to the system size. Furthermore, we find that intermediate degrees of parameter diversity and coupling strength jointly modulate either the waveform or the period of collective activity of the system, giving rise to the resonance for optimally suprathreshold signals. Finally, with low-dimensional reduced models, we explain the underlying mechanism of the observed resonance. Our results extend the scope of the diversity-induced resonance effect.

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.