Stochastic and vibrational resonance in complex networks of neurons

Optimal navigability of weighted human brain connectomes in physical space

Communication protocols in the brain connectome describe how to transfer information from one region to another. Typically, these protocols hinge on either the spatial distances between brain regions or the intensity of their connections. Yet, none of them combine both factors to achieve optimal efficiency. Here, we introduce a continuous spectrum of decentralized routing strategies that integrates link weights and the spatial embedding of connectomes to route signal transmission. We implemented the protocols on connectomes from individuals in two cohorts and on group-representative connectomes designed to capture weighted connectivity properties. We identified an intermediate domain of routing strategies, a sweet spot, where navigation achieves maximum communication efficiency at low transmission cost. This phenomenon is robust and independent of the particular configuration of weights. Our findings suggest an interplay between the intensity of neural connections and their topology and geometry that amplifies communicability, where weights play the role of noise in a stochastic resonance phenomenon. Such enhancement may support more effective responses to external and internal stimuli, underscoring the intricate diversity of brain functions.

Adaptive Signal Modulation Evolved by the Inherent Nonlinearity of Phase-Change Quantum-Dot String

To simulate a topological neural network handling weak signals via stochastic resonance (SR), it is necessary to introduce an inherent nonlinearity into nanoscale devices. We use the self-assembly method to successfully fabricate a phase-change quantum-dot string (PCQDS) crossing Pd/Nb:AlNO/AlNO/Nb:AlNO/Pd multilayer. The inherent nonlinearity of phase change couples with electron tunneling so that PCQDS responds to a long signal sequence in a modulated output style, in which the pulse pattern evolves to that enveloped by two sets of periodic wave characterized by neural action potential. We establish an SR mode consisting of several two-state systems in which dissipative tunneling is coupled to environment. Size oscillations owing to NbO QDs adaptively adjust barriers and wells, such that tunneling can be periodically modulated by either asymmetric energy or local temperature. When the external periodic signals are applied, the system first follows the forcing frequency. Subsequently, certain PCQDs oscillate independently and consecutively to produce complicated frequency and amplitude modulations.

Generation of stochastic mixed-mode oscillations in a pair of VDP oscillators with direct-indirect coupling

Environmental noise can lead to complex stochastic dynamical behavior in nonlinear systems. In this paper, we studied the phenomenon of a pair of Van der Pol (VDP) oscillators with direct-indirect coupling affected by Gaussian white noise. That is to say, a noise-induced equilibrium transition oscillation was observed in three types of different parameter regions, where the deterministic system had two kinds of stable equilibrium points. Meanwhile, with the noise intensity increasing, we found that the stochastic system will constantly switch between two stable equilibrium points. To analyze the stochastic behavior, we used the stochastic sensitivity equation and confidence ellipse method. When the confidence ellipsoid crossed the boundary of the attraction basin of the equilibrium point, the system entered into the state of stochastic mixed-mode oscillations, which was consistent with the simulation results.

Ultrasensitive vibrational resonance induced by small disturbances

We have found two kinds of ultrasensitive vibrational resonance in coupled nonlinear systems. It is particularly worth pointing out that this ultrasensitive vibrational resonance is transient behavior caused by transient chaos. Considering a long-term response, the system will transform from transient chaos to a periodic response. The pattern of vibrational resonance will also transform from ultrasensitive vibrational resonance to conventional vibrational resonance. This article focuses on the transient ultrasensitive vibrational resonance phenomenon. It is induced by a small disturbance of the high-frequency excitation and the initial simulation conditions, respectively. The damping coefficient and the coupling strength are the key factors to induce the ultrasensitive vibrational resonance. By increasing these two parameters, the vibrational resonance pattern can be transformed from ultrasensitive vibrational resonance to conventional vibrational resonance. The reason for different vibrational resonance patterns to occur lies in the state of the system response. The response usually presents transient chaotic behavior when the ultrasensitive vibrational resonance appears and the plot of the response amplitude vs the controlled parameters shows a highly fractalized pattern. When the response is periodic or doubly periodic, it usually corresponds to the conventional vibrational resonance. The ultrasensitive vibrational resonance not only occurs at the excitation frequency, but it also occurs at some more nonlinear frequency components. The ultrasensitive vibrational resonance as transient behavior and the transformation of vibrational resonance patterns are new phenomena in coupled nonlinear systems.

Synchronization of Complex Dynamical Networks with Stochastic Links Dynamics

The mean square synchronization problem of the complex dynamical network (CDN) with the stochastic link dynamics is investigated. In contrast to previous literature, the CDN considered in this paper can be viewed as consisting of two subsystems coupled to each other. One subsystem consists of all nodes, referred to as the nodes subsystem, and the other consists of all links, referred to as the network topology subsystem, where the weighted values can quantitatively reflect changes in the network's topology. Based on the above understanding of CDN, two vector stochastic differential equations with Brownian motion are used to model the dynamic behaviors of nodes and links, respectively. The control strategy incorporates not only the controller in the nodes but also the coupling term in the links, through which the CDN is synchronized in the mean-square sense. Meanwhile, the dynamic stochastic signal is proposed in this paper, which is regarded as the auxiliary reference tracking target of links, such that the links can track the reference target asymptotically when synchronization occurs in nodes. This implies that the eventual topological structure of CDN is stochastic. Finally, a comparison simulation example confirms the superiority of the control strategy in this paper.

Subsensory stochastic electrical stimulation targeting muscle afferents alters gait control during locomotor adaptations to haptic perturbations

Subsensory noise stimulation targeting sensory receptors has been shown to improve balance control in healthy and impaired individuals. However, the potential for application of this technique in other contexts is still unknown. Gait control and adaptation rely heavily on the input from proprioceptive organs in the muscles and joints. Here we investigated the use of subsensory noise stimulation as a means to influence motor control by altering proprioception during locomotor adaptations to forces delivered by a robot. The forces increase step length unilaterally and trigger an adaptive response that restores the original symmetry. Healthy participants performed two adaptation experiments, one with stimulation applied to the hamstring muscles and one without. We found that participants adapted faster but to a lesser extent when undergoing stimulation. We argue that this behavior is because of the dual effect that the stimulation has on the afferents encoding position and velocity in the muscle spindles.

Controlling the spontaneous firing behavior of a neuron with astrocyte

Mounting evidence in recent years suggests that astrocytes, a sub-type of glial cells, not only serve metabolic and structural support for neurons and synapses but also play critical roles in the regulation of proper functioning of the nervous system. In this work, we investigate the effect of astrocytes on the spontaneous firing activity of a neuron through a combined model that includes a neuron-astrocyte pair. First, we show that an astrocyte may provide a kind of multistability in neuron dynamics by inducing different firing modes such as random and bursty spiking. Then, we identify the underlying mechanism of this behavior and search for the astrocytic factors that may have regulatory roles in different firing regimes. More specifically, we explore how an astrocyte can participate in the occurrence and control of spontaneous irregular spiking activity of a neuron in random spiking mode. Additionally, we systematically investigate the bursty firing regime dynamics of the neuron under the variation of biophysical facts related to the intracellular environment of the astrocyte. It is found that an astrocyte coupled to a neuron can provide a control mechanism for both spontaneous firing irregularity and burst firing statistics, i.e., burst regularity and size.

Interlayer Connectivity Affects the Coherence Resonance and Population Activity Patterns in Two-Layered Networks of Excitatory and Inhibitory Neurons

The firing patterns of neuronal populations often exhibit emergent collective oscillations, which can display substantial regularity even though the dynamics of individual elements is very stochastic. One of the many phenomena that is often studied in this context is coherence resonance, where additional noise leads to improved regularity of spiking activity in neurons. In this work, we investigate how the coherence resonance phenomenon manifests itself in populations of excitatory and inhibitory neurons. In our simulations, we use the coupled FitzHugh-Nagumo oscillators in the excitable regime and in the presence of neuronal noise. Formally, our model is based on the concept of a two-layered network, where one layer contains inhibitory neurons, the other excitatory neurons, and the interlayer connections represent heterotypic interactions. The neuronal activity is simulated in realistic coupling schemes in which neurons within each layer are connected with undirected connections, whereas neurons of different types are connected with directed interlayer connections. In this setting, we investigate how different neurophysiological determinants affect the coherence resonance. Specifically, we focus on the proportion of inhibitory neurons, the proportion of excitatory interlayer axons, and the architecture of interlayer connections between inhibitory and excitatory neurons. Our results reveal that the regularity of simulated neural activity can be increased by a stronger damping of the excitatory layer. This can be accomplished with a higher proportion of inhibitory neurons, a higher fraction of inhibitory interlayer axons, a stronger coupling between inhibitory axons, or by a heterogeneous configuration of interlayer connections. Our approach of modeling multilayered neuronal networks in combination with stochastic dynamics offers a novel perspective on how the neural architecture can affect neural information processing and provide possible applications in designing networks of artificial neural circuits to optimize their function via noise-induced phenomena.

Synchronization of the neurons coupled with sequential developing electrical and chemical synapses

There is some evidence representing the sequential formation and elimination of electrical and chemical synapses in particular brain regions. Relying on this feature, this paper presents a purely mathematical modeling study on the synchronization among neurons connected by transient electrical synapses transformed to chemical synapses over time. This deletion and development of synapses are considered consecutive. The results represent that the transient synapses lead to burst synchronization of the neurons while the neurons are resting when both synapses exist constantly. The period of the transitions and also the time of presence of electrical synapses to chemical ones are effective on the synchronization. The larger synchronization error is obtained by increasing the transition period and the time of chemical synapses' existence.

Vibrational and stochastic resonances in driven nonlinear systems: part 2

Nonlinearity is ubiquitous in both natural and engineering systems. The resultant dynamics has emerged as a multidisciplinary field that has been very extensively investigated, due partly to the potential occurrence of nonlinear phenomena in all branches of sciences, engineering and medicine. Driving nonlinear systems with external excitations can yield a plethora of intriguing and important phenomena-one of the most prominent being that of resonance. In the presence of additional harmonic or stochastic excitation, two exotic forms of resonance can arise: vibrational resonance or stochastic resonance, respectively. Several promising state-of-the-art technologies that were not covered in part 2 of this theme issue are discussed here. They include inter alia the improvement of image quality, the design of machines and devices that exert vibrations on materials, the harvesting of energy from various forms of ambient vibration and control of aerodynamic instabilities. They form an important part of the theme issue as a whole, which is dedicated to an overview of vibrational and stochastic resonances in driven nonlinear systems. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.