Vibrational resonance in a scale-free network with different coupling schemes

Neuronal synchronization in long-range time-varying networks

We study synchronization in neuronal ensembles subject to long-range electrical gap junctions which are time-varying. As a representative example, we consider Hindmarsh-Rose neurons interacting based upon temporal long-range connections through electrical couplings. In particular, we adopt the connections associated with the direct 1-path network to form a small-world network and follow-up with the corresponding long-range network. Further, the underlying direct small-world network is allowed to temporally change; hence, all long-range connections are also temporal, which makes the model much more realistic from the neurological perspective. This time-varying long-range network is formed by rewiring each link of the underlying 1-path network stochastically with a characteristic rewiring probability p_r, and accordingly all indirect k(>1)-path networks become temporal. The critical interaction strength to reach complete neuronal synchrony is much lower when we take up rapidly switching long-range interactions. We employ the master stability function formalism in order to characterize the local stability of the state of synchronization. The analytically derived stability condition for the complete synchrony state agrees well with the numerical results. Our work strengthens the understanding of time-varying long-range interactions in neuronal ensembles.

Stochastic and vibrational resonance in complex networks of neurons

The concept of resonance in nonlinear systems is crucial and traditionally refers to a specific realization of maximum response provoked by a particular external perturbation. Depending on the system and the nature of perturbation, many different resonance types have been identified in various fields of science. A prominent example is in neuroscience where it has been widely accepted that a neural system may exhibit resonances at microscopic, mesoscopic and macroscopic scales and benefit from such resonances in various tasks. In this context, the two well-known forms are stochastic and vibrational resonance phenomena which manifest that detection and propagation of a feeble information signal in neural structures can be enhanced by additional perturbations via these two resonance mechanisms. Given the importance of network architecture in proper functioning of the nervous system, we here present a review of recent studies on stochastic and vibrational resonance phenomena in neuronal media, focusing mainly on their emergence in complex networks of neurons as well as in simple network structures that represent local behaviours of neuron communities. From this perspective, we aim to provide a secure guide by including theoretical and experimental approaches that analyse in detail possible reasons and necessary conditions for the appearance of stochastic resonance and vibrational resonance in neural systems. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.

Vibrational resonance in a neuron-astrocyte coupled model

Recent findings have revealed that not only neurons but also astrocytes, a special type of glial cells, are major players of neuronal information processing. It is now widely accepted that they contribute to the regulation of their microenvironment by cross-talking with neurons via gliotransmitters. In this context, we here study the phenomenon of vibrational resonance in neurons by considering their interaction with astrocytes. Our analysis of a neuron-astrocyte pair reveals that intracellular dynamics of astrocytes can induce a double vibrational resonance effect in the weak signal detection performance of a neuron, exhibiting two distinct wells centred at different high-frequency driving amplitudes. We also identify the underlying mechanism of this behaviour, showing that the interaction of widely separated time scales of neurons, astrocytes and driving signals is the key factor for the emergence and control of double vibrational resonance. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.

Study of vibrational resonance in nonlinear signal processing

Vibrational resonance (VR) intentionally applies high-frequency periodic vibrations to a nonlinear system, in order to obtain enhanced efficiency for a number of information processing tasks. Note that VR is analogous to stochastic resonance where enhanced processing is sought via purposeful addition of a random noise instead of deterministic high-frequency vibrations. Comparatively, due to its ease of implementation, VR provides a valuable approach for nonlinear signal processing, through detailed modalities that are still under investigation. In this paper, VR is investigated in arrays of nonlinear processing devices, where a range of high-frequency sinusoidal vibrations of the same amplitude at different frequencies are injected and shown capable of enhancing the efficiency for estimating unknown signal parameters or for detecting weak signals in noise. In addition, it is observed that high-frequency vibrations with differing frequencies can be considered, at the sampling times, as independent random variables. This property allows us here to develop a probabilistic analysis-much like in stochastic resonance-and to obtain a theoretical basis for the VR effect and its optimization for signal processing. These results provide additional insight for controlling the capabilities of VR for nonlinear signal processing. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.

Entropic vibrational resonance

We demonstrate the existence of vibrational resonance associated with the presence of an uneven boundary. When the motion of a Brownian particle is confined in a region with an uneven boundary, constrained to a double cavity, a high-frequency signal may produce a peak in the spectral power amplification of the other low-frequency signal and therefore to the appearance of the vibrational resonance phenomenon. The mechanism of vibrational resonance in constrained boundaries is different from that in energetic potentials and is termed entropic vibrational resonance (EVR). The EVR can be observed even if the bias force is absent in any direction. Through careful analysis, we clarify two types of mechanisms of the EVR. The one mechanism is ascribed to the transition from a bistable system to a monostable system, and the other corresponds to the match between the escape rate and the natural frequency of the low-frequency signal. Our work merges the vibrational resonance with an uneven boundary, thus extending the scope of the vibrational resonance and shedding new light on the concept of resonance.