Coherence resonance in influencer networks

Emergence of chaotic cluster synchronization in heterogeneous networks

Many real-world complex systems rely on cluster synchronization to function properly. A cluster of nodes exhibits synchronous behavior, while others behave erratically. Predicting the emergence of these clusters and understanding the mechanism behind their structure and variation in response to a parameter change is a daunting task in networks that lack symmetry. We unravel the mechanism for the emergence of cluster synchronization in heterogeneous random networks. We develop heterogeneous mean-field approximation together with a self-consistent theory to determine the onset and stability of the cluster. Our analysis shows that cluster synchronization occurs in a wide variety of heterogeneous networks, node dynamics, and coupling functions. The results could lead to a new understanding of the dynamical behavior of networks ranging from neural to social.

Exponentially Long Transient Time to Synchronization of Coupled Chaotic Circle Maps in Dense Random Networks

We study the transition to synchronization in large, dense networks of chaotic circle maps, where an exact solution of the mean-field dynamics in the infinite network and all-to-all coupling limit is known. In dense networks of finite size and link probability of smaller than one, the incoherent state is meta-stable for coupling strengths that are larger than the mean-field critical coupling. We observe chaotic transients with exponentially distributed escape times and study the scaling behavior of the mean time to synchronization.

Notes on resonant and synchronized states in complex networks

Synchronization and resonance on networks are some of the most remarkable collective dynamical phenomena. The network topology, or the nature and distribution of the connections within an ensemble of coupled oscillators, plays a crucial role in shaping the local and global evolution of the two phenomena. This article further explores this relationship within a compact mathematical framework and provides new contributions on certain pivotal issues, including a closed bound for the average synchronization time in arbitrary topologies; new evidences of the effect of the coupling strength on this time; exact closed expressions for the resonance frequencies in terms of the eigenvalues of the Laplacian matrix; a measure of the effectiveness of an influencer node's impact on the network; and, finally, a discussion on the existence of a resonant synchronized state. Some properties of the solution of the linear swing equation are also discussed within the same setting. Numerical experiments conducted on two distinct real networks-a social network and a power grid-illustrate the significance of these results and shed light on intriguing aspects of how these processes can be interpreted within networks of this kind.

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.

Emergent hypernetworks in weakly coupled oscillators

Networks of weakly coupled oscillators had a profound impact on our understanding of complex systems. Studies on model reconstruction from data have shown prevalent contributions from hypernetworks with triplet and higher interactions among oscillators, in spite that such models were originally defined as oscillator networks with pairwise interactions. Here, we show that hypernetworks can spontaneously emerge even in the presence of pairwise albeit nonlinear coupling given certain triplet frequency resonance conditions. The results are demonstrated in experiments with electrochemical oscillators and in simulations with integrate-and-fire neurons. By developing a comprehensive theory, we uncover the mechanism for emergent hypernetworks by identifying appearing and forbidden frequency resonant conditions. Furthermore, it is shown that microscopic linear (difference) coupling among units results in coupled mean fields, which have sufficient nonlinearity to facilitate hypernetworks. Our findings shed light on the apparent abundance of hypernetworks and provide a constructive way to predict and engineer their emergence.

Networks with higher-order interactions are relevant to variety of real-world applications, they can be good description of data even if the system has only pairwise interactions. The authors uncover the hypernetwork emergence in coupled nonlinear oscillators and electrochemical experiments.

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.

White-noise-induced double coherence resonances in reduced Hodgkin-Huxley neuron model near subcritical Hopf bifurcation

Coherence resonance (CR) describes a counterintuitive phenomenon in which the optimal oscillatory responses in nonlinear systems are shaped by a suitable noise amplitude. This phenomenon has been observed in neural systems. In this research, the generation of double coherence resonances (DCRs) due to white noise is investigated in a three-dimensional reduced Hodgkin-Huxley neuron model with multiple-timescale feature. We show that additive white noise can induce DCRs from the resting state near a subcritical Hopf bifurcation. The appearance of DCRs is related to the changes of the firing pattern aroused by the increases of the noise amplitude. The underlying dynamical mechanisms for the appearance of the DCRs and the changes of the firing pattern are interpreted using the phase space analysis and the dynamics of the stable focus-node near the subcritical Hopf bifurcation. We find that the multiple-timescale dynamics is essential for generating the DCRs and different firing patterns. The results not only present a case in which noise can induce DCRs near a Hopf bifurcation but also provide its dynamical mechanism, which enriches the phenomena in nonlinear dynamics and provides further understanding on the roles of noise in neural systems with multiple-timescale feature.

Noise-induced network bursts and coherence in a calcium-mediated neural network

Noise-induced population bursting has been widely identified to play important roles in information processes. We construct a mathematical model for a random and sparse heterogeneous neural network where bursting can be induced from a resting state by a global stochastic stimulus. Importantly, the noise-induced bursting dynamics of this network are mediated by calcium conductance. We use two spectral measures to evaluate network coherence in the context of the network bursts, the spike trains of all neurons, and the individual bursts of all neurons. Our results show that the coherence of the network is optimized by an optimal level of the stochastic stimulus, which is known as coherence resonance (CR). We also demonstrate that the interplay of the calcium conductance and noise intensity can modify the degree of CR.