Mechanism for explosive synchronization of neural networks

Explosive transitions in coupled Lorenz oscillators

We study the transition to synchronization in an ensemble of chaotic oscillators that are interacting on a star network. These oscillators possess an invariant symmetry and we study emergent behavior by introducing the timescale variations in the dynamics of the nodes and the hub. If the coupling preserves the symmetry, the ensemble exhibits consecutive explosive transitions, each one associated with a hysteresis. The first transition is the explosive synchronization from a desynchronized state to a synchronized state which occurs discontinuously with the formation of intermediate clusters. These clusters appear because of the driving-induced multistability and the resulting attractors exhibit intermittent synchrony (antisynchrony). The second transition is the explosive death that occurs as a result of stabilization of the stable fixed points. However, if the symmetry is not preserved, the system again makes a first-order transition from an oscillatory state to death, namely, an explosive death. These transitions are studied with the help of the master stability functions, Lyapunov exponents, and the stability analysis.

Optimal input reverberation and homeostatic self-organization toward the edge of synchronization

Transient or partial synchronization can be used to do computations, although a fully synchronized network is sometimes related to the onset of epileptic seizures. Here, we propose a homeostatic mechanism that is capable of maintaining a neuronal network at the edge of a synchronization transition, thereby avoiding the harmful consequences of a fully synchronized network. We model neurons by maps since they are dynamically richer than integrate-and-fire models and more computationally efficient than conductance-based approaches. We first describe the synchronization phase transition of a dense network of neurons with different tonic spiking frequencies coupled by gap junctions. We show that at the transition critical point, inputs optimally reverberate through the network activity through transient synchronization. Then, we introduce a local homeostatic dynamic in the synaptic coupling and show that it produces a robust self-organization toward the edge of this phase transition. We discuss the potential biological consequences of this self-organization process, such as its relation to the Brain Criticality hypothesis, its input processing capacity, and how its malfunction could lead to pathological synchronization and the onset of seizure-like activity.

Energy-guided synapse coupling between neurons under noise

From a physical viewpoint, any external stimuli including noise disturbance can inject energy into the media, and the electric response is regulated by the equivalent electric stimulus. For example, mode transition in electric activities in neurons occurs and kinds of spatial patterns are formed during the wave propagation. In this paper, a feasible criterion is suggested to explain and control the growth of electric synapse and memristive synapse between Hindmarsh-Rose neurons in the presence of noise. It is claimed that synaptic coupling can be enhanced adaptively due to energy diversity, and the coupling intensity is increased to a saturation value until two neurons reach certain energy balance. Two identical neurons can reach perfect synchronization when electric synapse coupling is further increased. This scheme is also considered in a chain neural network and uniform noise is applied on all neurons. However, reaching synchronization becomes difficult for neurons in presenting spiking, bursting, and chaotic and periodic patterns, even when the local energy balance is corrupted to continue further growth of the coupling intensity. In the presence of noise, energy diversity becomes uncertain because of spatial diversity in excitability, and development of regular patterns is blocked. The similar scheme is used to control the growth of memristive synapse for neurons, and the synchronization stability and pattern formation are controlled by the energy diversity among neurons effectively. These results provide possible guidance for knowing the biophysical mechanism for synapse growth and energy flow can be applied to control the synchronous patterns between neurons.

Long-range connections are crucial for synchronization transition in a computational model of Drosophila brain dynamics

The synchronization transition type has been the focus of attention in recent years because it is associated with many functional characteristics of the brain. In this paper, the synchronization transition in neural networks with sleep-related biological drives in Drosophila is investigated. An electrical synaptic neural network is established to research the difference between the synchronization transition of the network during sleep and wake, in which neurons regularly spike during sleep and chaotically spike during wake. The synchronization transition curves are calculated mainly using the global instantaneous order parameters S. The underlying mechanisms and types of synchronization transition during sleep are different from those during wake. During sleep, regardless of the network structure, a frustrated (discontinuous) transition can be observed. Moreover, the phenomenon of quasi periodic partial synchronization is observed in ring-shaped regular network with and without random long-range connections. As the network becomes dense, the synchronization of the network only needs to slightly increase the coupling strength g. While during wake, the synchronization transition of the neural network is very dependent on the network structure, and three mechanisms of synchronization transition have emerged: discontinuous synchronization (explosive synchronization and frustrated synchronization), and continuous synchronization. The random long-range connections is the main topological factor that plays an important role in the resulting synchronization transition. Furthermore, similarities and differences are found by comparing synchronization transition research for the Hodgkin-Huxley neural network in the beta-band and gammma-band, which can further improve the synchronization phase transition research of biologically motivated neural networks. A complete research framework can also be used to study coupled nervous systems, which can be extended to general coupled dynamic systems.

Assortativity-induced explosive synchronization in a complex neuronal network

In this study, we consider a scale-free network of nonidentical Chialvo neurons, coupled through electrical synapses. For sufficiently strong coupling, the system undergoes a transition from completely out of phase synchronized to phase synchronized state. The principal focus of this study is to investigate the effect of the degree of assortativity over the synchronization transition process. It is observed that, depending on assortativity, bistability between two asymptotically stable states allows one to develop a hysteresis loop which transforms the phase transition from second order to first order. An expansion in the area of hysteresis loop is noticeable with increasing degree-degree correlation in the network. Our study also reveals that effective frequencies of nodes simultaneously go through a continuous or sudden transition to the synchronized state with the corresponding phases. Further, we examine the robustness of the results under the effect of network size and average degree, as well as diverse frequency setup. Finally, we investigate the dynamical mechanism in the process of generating explosive synchronization. We observe a significant impact of lower degree nodes behind such phenomena: in a positive assortative network the low degree nodes delay the synchronization transition.

Thermal Hysteresis Involving Reversible Self-Catalytic Reactions

Hysteresis is ubiquitous in nature and biology. It appears in ferromagnetism, ferroelectrism, traffic congestion, river sedimentation, electronics, thermoresponses, cell division, differentiation, and apoptosis. Hysteresis phenomena are beyond equilibrium and involve nonlinear, bistable, time delay, and memory events, which are described in input/output profiles by different outputs during continuous decreases and increases in input intensity. Although hysteresis profiles in these phenomena appear similar, the mechanisms underlying them are complex, and their basic understanding is desired. In this Account, I describe thermal hysteresis caused by molecules dispersed in dilute solutions containing optically active helicene oligomers, which form homo- and heterodouble helices, the cooling and heating processes of which cause different structural changes with regard to their relative concentrations. Reversible self-catalytic reactions are involved in the formation of a double helix, which catalyzes its own formation. The reactions accelerate as they progress, in contrast to ordinary reactions, which exhibit monotonic retardation as they progress. Thermal hysteresis involving reversible self-catalytic reactions exhibits notable phenomena, when various cooling/heating inputs are applied during the reaction; these phenomena are shown herein with profiles of experimental results of Δε outputs obtained by circular dichroism (CD) plotted against temperature inputs. Thermal hysteresis is discussed in terms of (1) two states of the homodouble helix and a random coil involving one reversible self-catalytic reaction and (2) three states of enantiomeric heterodouble helices and a random coil involving two reversible self-catalytic reactions. Repeated cooling and heating processes provide the same stable thermal hysteresis loops, when the initial and final high-temperature states are under equilibrium, and nonloop and unstable thermal hysteresis appears when whole the systems are beyond equilibrium. Diverse thermal hysteresis loops are obtained under different temperature change conditions for different oligomers. The mechanism of thermal hysteresis involves different macroscopic mechanisms at a fixed temperature, when the relative concentrations of substrates/products and the reaction direction differ. Microscopic mechanisms, which are shown by energy diagrams, are fixed at a temperature irrespective of cooling or heating. A comparison of thermal hysteresis loops and equilibrium curves provides distances to the metastable states on the loops from equilibrium, and reactions occur from the metastable states toward equilibrium. Notable phenomena described herein include bistability, high sensitivity to small concentration changes, equilibrium crossing, three-state one-directional structural change caused by a single heating procedure, reaction shortcuts, the memory effect on thermal history, figure-eight thermal hysteresis, chemical oscillation, stable and unstable thermal hysteresis, double-helix formation only under heating, and chiral symmetry breaking.

Transition to synchronization in heterogeneous inhibitory neural networks with structured synapses

Inhibitory neurons form an extensive network involved in the development of different rhythms in the cerebral cortex. A transition from an incoherent state, where all inhibitory neurons fire unrelated to each other, to a synchronized or locked state, where all or most neurons define a tight firing pattern, is maybe the most salient process to analyze when considering neuronal rhythms. In this work, we analyzed whether different patterns of effective synaptic connectivity may support a first-order-like transition in this path to synchronization. Such an "explosive" phenomenon may be relevant in neural processes, as normal cognitive processing in different tasks and some neurological disorders manifest an increased power in many neuronal rhythms, supported by an extended concerted spiking activity and an abrupt change to this state. Furthermore, we built an adaptive mechanism that supports the generation of this kind of network, which rapidly creates the underlying structure based on the ongoing firing statistics.