a b s t r a c tThe propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and critical phenomena of networked coevolution spreading are extremely important, which provide theoretical foundations for us to control epidemic spreading, predict collective behaviors in social systems, and so on. The coevolution spreading dynamics in complex networks has thus attracted much attention in many disciplines. In this review, we introduce recent progress in the study of coevolution spreading dynamics, emphasizing the contributions from the perspectives of statistical mechanics and network science. The theoretical methods, critical phenomena, phase transitions, interacting mechanisms, and effects of network topology for four representative types of coevolution spreading mechanisms, including the coevolution of biological contagions, social contagions, epidemic-awareness, and epidemic-resources, are presented in detail, and the challenges in this field as well as open issues for future studies are also discussed.

Cortical neural circuits display highly irregular spiking in individual neurons but variably sized collective firing, oscillations and critical avalanches at the population level, all of which have functional importance for information processing. Theoretically, the balance of excitation and inhibition inputs is thought to account for spiking irregularity and critical avalanches may originate from an underlying phase transition. However, the theoretical reconciliation of these multilevel dynamic aspects in neural circuits remains an open question. Herein, we study excitation-inhibition (E-I) balanced neuronal network with biologically realistic synaptic kinetics. It can maintain irregular spiking dynamics with different levels of synchrony and critical avalanches emerge near the synchronous transition point. We propose a novel semi-analytical mean-field theory to derive the field equations governing the network macroscopic dynamics. It reveals that the E-I balanced state of the network manifesting irregular individual spiking is characterized by a macroscopic stable state, which can be either a fixed point or a periodic motion and the transition is predicted by a Hopf bifurcation in the macroscopic field. Furthermore, by analyzing public data, we find the coexistence of irregular spiking and critical avalanches in the spontaneous spiking activities of mouse cortical slice in vitro, indicating the universality of the observed phenomena. Our theory unveils the mechanism that permits complex neural activities in different spatiotemporal scales to coexist and elucidates a possible origin of the criticality of neural systems. It also provides a novel tool for analyzing the macroscopic dynamics of E-I balanced networks and its relationship to the microscopic counterparts, which can be useful for large-scale modeling and computation of cortical dynamics.

During an epidemic control, the containment of the disease is usually achieved through increasing devoted resource to shorten the duration of infectiousness. However, the impact of this resource expenditure has not been studied quantitatively. Using the well-documented cholera data, we observe empirically that the recovery rate which is related to the duration of infectiousness has a strong positive correlation with the average resource devoted to the infected individuals. By incorporating this relation we build a novel model and find that insufficient resource leads to an abrupt increase in the infected population size, which is in marked contrast with the continuous phase transitions believed previously. Counterintuitively, this abrupt phase transition is more pronounced in the less contagious diseases, which usually correspond to the most fatal ones. Furthermore, we find that even for a single infection source, public resource needs to meet a significant amount, which is proportional to the whole population size to ensure epidemic containment. Our findings provide a theoretical foundation for efficient epidemic containment strategies in the early stage.In recent 20 years, epidemic outbreaks such as Ebola, SARS, H1N1, HIV etc., had detrimental * These three authors contributed equally †

Critical transition, a phenomenon that a system shifts suddenly from one state to another, occurs in many real-world complex networks. We propose an analytical framework for exactly predicting the critical transition in a complex networked system subjected to noise effects. Our prediction is based on the characteristic return time of a simple one-dimensional system derived from the original higher-dimensional system. This characteristic time, which can be easily calculated using network data, allows us to systematically separate the respective roles of dynamics, noise and topology of the underlying networked system. We find that the noise can either prevent or enhance critical transitions, playing a key role in compensating the network structural defect which suffers from either internal failures or environmental changes, or both. Our analysis of realistic or artificial examples reveals that the characteristic return time is an effective indicator for forecasting the sudden deterioration of complex networks.

Detecting critical transitions in the case of moderate or strong noise (collectively referred to as big noise) is challenging, since such noise can make a critical transition point far from the bifurcation point, leading to the failure of traditional small-noise methods. To handle this tough issue, we first transform a generic noisy system into a linear set of binomial moment equations (BMEs). Then, we can solve a closed set of BMEs obtained by truncation and use the resulting binomial moments to reconstruct a joint probability distribution of the state variables of the original system. Third, we derive a leading indicator from the closed set of BMEs. Importantly, the reconstructed distribution determines the way of critical transition (i.e., critical transition is distribution transition rather than state transition in the strong-noise case) as the system comes close to the critical transition point, whereas the derived indicator anticipates when the distribution transition occurs. Our theory has broad applications, and artificial and data examples exhibit its power.

Rich spatiotemporal dynamics of cortical activity, including complex and diverse wave patterns, have been identified during unconscious and conscious brain states. Yet, how these activity patterns emerge across different levels of wakefulness remain unclear. Here we study the evolution of wave patterns utilizing data from high spatiotemporal resolution optical voltage imaging of mice transitioning from barbiturate-induced anesthesia to wakefulness (N = 5) and awake mice (N = 4). We find that, as the brain transitions into wakefulness, there is a reduction in hemisphere-scale voltage waves, and an increase in local wave events and complexity. A neural mass model recapitulates the essential cellular-level features and shows how the dynamical competition between global and local spatiotemporal patterns and long-range connections can explain the experimental observations. These mechanisms possibly endow the awake cortex with enhanced integrative processing capabilities.

Gamma oscillation in neural circuits is believed to associate with effective learning in the brain, while the underlying mechanism is unclear. This paper aims to study how spike-timing-dependent plasticity (STDP), a typical mechanism of learning, with its interaction with gamma oscillation in neural circuits, shapes the network dynamics properties and the network structure formation. We study an excitatory-inhibitory (E-I) integrate-and-fire neuronal network with triplet STDP, heterosynaptic plasticity, and a transmitter-induced plasticity. Our results show that the performance of plasticity is diverse in different synchronization levels. We find that gamma oscillation is beneficial to synaptic potentiation among stimulated neurons by forming a special network structure where the sum of excitatory input synaptic strength is correlated with the sum of inhibitory input synaptic strength. The circuit can maintain E-I balanced input on average, whereas the balance is temporal broken during the learning-induced oscillations. Our study reveals a potential mechanism about the benefits of gamma oscillation on learning in biological neural circuits.

Cortical neural networks exhibit high internal variability in spontaneous dynamic activities and they can robustly and reliably respond to external stimuli with multilevel features–from microscopic irregular spiking of neurons to macroscopic oscillatory local field potential. A comprehensive study integrating these multilevel features in spontaneous and stimulus–evoked dynamics with seemingly distinct mechanisms is still lacking. Here, we study the stimulus–response dynamics of biologically plausible excitation–inhibition (E–I) balanced networks. We confirm that networks around critical synchronous transition states can maintain strong internal variability but are sensitive to external stimuli. In this dynamical region, applying a stimulus to the network can reduce the trial-to-trial variability and shift the network oscillatory frequency while preserving the dynamical criticality. These multilevel features widely observed in different experiments cannot simultaneously occur in non-critical dynamical states. Furthermore, the dynamical mechanisms underlying these multilevel features are revealed using a semi-analytical mean-field theory that derives the macroscopic network field equations from the microscopic neuronal networks, enabling the analysis by nonlinear dynamics theory and linear noise approximation. The generic dynamical principle revealed here contributes to a more integrative understanding of neural systems and brain functions and incorporates multimodal and multilevel experimental observations. The E–I balanced neural network in combination with the effective mean-field theory can serve as a mechanistic modeling framework to study the multilevel neural dynamics underlying neural information and cognitive processes.