System Size Resonance Research Articles

Vibrational resonance in globally coupled bistable systems under the noise background

Effects of system size, coupling strength, and noise on vibrational resonance (VR) of globally coupled bistable systems are investigated. The power spectral amplifications obtained by the three methods all show that the VR exists over a wide range of parameter values. The increase in system size induces and enhances the VR, while the increase in noise intensity suppresses and eventually eliminates the VR. Both the stochastic resonance and the system size resonance can coexist with the VR in different parameter regions. This research has potential applications to the weak signal detection process in stochastic multi-body systems.

Array enhanced stochastic resonance for augmented energy harvesting

Research studies on vibration energy harvesting have shown from time to time that bistable harvesters offer a lucrative solution for harnessing substantial magnitude of power across a broad range of frequencies. This exciting potential of bistable harvesters has bred interest towards investigating the possibility of enhancement in power by coupling multiple of them. In this regard, the present work analyzes the behavior of a 1-D array of bistable piezoelectric harvesters mechanically coupled in the nearest-neighbor configuration under a noise perturbed periodic base excitation. The numerical study reports a resonant-like behavior of the total power with system size for certain noise levels of excitation. The parametric regimes to which the system size resonance effect is confined have been identified. The present work attempts to provide an intuitive understanding into the role of system size on the total harvested power under a noisy environment. Inferences drawn from the results of this work shall help in designing a harvesting system to realize broadband power generation.

Optimal system size for complex dynamics in random neural networks near criticality

In this article, we consider a model of dynamical agents coupled through a random connectivity matrix, as introduced by Sompolinsky et al. [Phys. Rev. Lett. 61(3), 259–262 (1988)] in the context of random neural networks. When system size is infinite, it is known that increasing the disorder parameter induces a phase transition leading to chaotic dynamics. We observe and investigate here a novel phenomenon in the sub-critical regime for finite size systems: the probability of observing complex dynamics is maximal for an intermediate system size when the disorder is close enough to criticality. We give a more general explanation of this type of system size resonance in the framework of extreme values theory for eigenvalues of random matrices.

Phase-noise-induced resonance in arrays of coupled excitable neural models.

Recently, it is observed that, in a single neural model, phase noise (time-varying signal phase) arising from an external stimulating signal can induce regular spiking activities even if the signal is subthreshold. In addition, it is also uncovered that there exists an optimal phase noise intensity at which the spiking rhythm coincides with the frequency of the subthreshold signal, resulting in a phase-noise-induced resonance phenomenon. However, neurons usually do not work alone, but are connected in the form of arrays or blocks. Therefore, we study the spiking activity induced by phase noise in arrays of globally and locally coupled excitable neural models. We find that there also exists an optimal phase noise intensity for generating large neural response and such an optimal value is significantly decreased compared to an isolated single neuron case, which means the detectability in response to the subthreshold signal of neurons is sharply improved because of the coupling. In addition, we reveal two new resonance behaviors in the neuron ensemble with the presence of phase noise: there exist optimal values of both coupling strength and system size, where the coupled neurons generate regular spikes under subthreshold stimulations, which are called as coupling strength and system size resonance, respectively. Finally, the dependence of phase-noise-induced resonance on signal frequency is also examined.

External perturbation manifested system size resonance in a mesoscopic hormone signaling model

In mesoscopic reaction systems that contain only finite number of reactants, molecular fluctuation (or the so called internal noise), which can be characterized by the system size, plays an important role in nonlinear systems. In this work, the effect of internal noise is studied in a mesoscopic hormone signaling model with the presence of external perturbations (noise or signal). Simulation results reveal that the internal noise can play a constructive role to optimize the regularity of the noise induced internal signal only when external perturbation is present. This is a novel external perturbations induced system size resonance, which indicates that in complex mesoscopic systems, the system can automatically avoid the destructive environmental effects by tuning its size. Such kind of nontrivial cooperative effect may attribute to the fact that external perturbations broadened the regulation scope of the key mutual feedback. Therefore, current finding is of practical significance for similar physiological systems where the intercellular regulation plays the dominate role for signaling.

Non-Gaussian noise- and system-size-induced coherence resonance of calcium oscillations in an array of coupled cells

In this paper, by introducing a particular kind of parametric non-Gaussian noise (NGN) via the inositol triphosphate (IP3), we study the effect of the NGN’s deviation q from the Gaussian noise and its correlation time τ, as well as the cell number N on the intercellular Ca2+ oscillations in an array of bi-directionally coupled cells. It is found that Ca2+ oscillations may become the most ordered in time when q, τ or N is varied, which characterize the phenomenon of coherence resonance and system size resonance. These results show that the temporal coherence of the Ca2+ oscillation can be enhanced when the NGN or the cell number is optimal. This work extends the study of the NGN in calcium systems and provides new insight into the roles of the NGN in the intercellular Ca2+ oscillations in the coupled cells.

THE ROLE OF INTERNAL NOISE FOR OPTIMAL INTRACELLULAR CALCIUM SIGNALING IN COUPLED BIOLOGICAL CELL SYSTEM

We have studied the role of internal noise for intracellular calcium signaling in coupled biological cell system. It is found that internal noise can induce calcium oscillations and the performance of such oscillations shows two peaks with the variation of the cell size-Ω for any cell chain length-N, indicating the occurrence of system size bi-resonance or internal noise stochastic bi-resonance, which may be very relevant to the canard explosion. We also find that there exists an optimal cell chain length-N for the first peak at which the collective calcium oscillations show the best performance, it is also a phenomenon of "system size resonance". It is interesting to note that one of the optimal cell sizes is present at Ω ~ 103μm3, which is close to a real living cell size in vivo.

Influence of interaction delays on noise-induced coherence in excitable systems

Influence of the interaction time delay on the noise-induced system size resonance in a system of all-to-all electrically coupled FitzHugh-Nagumo excitable neurons is studied. It is observed that small time lags decrease and that large time lags increase the coherence of spiking. Bifurcations of the system's stationary state are used to explain the observed nonmonotonic dependence of coherence on the time lag.

Noise as control parameter in networks of excitable media: Role of the network topology

We analyze coupled FitzHugh-Nagumo oscillators on various network topologies, in particular random diluted and scale-free topologies, under the influence of noise. Similarly to globally coupled excitable units, noise acts as control parameter: changing monotonically its strength, the collective dynamical behavior varies from stable equilibrium solutions to coherent firing of a large fraction, and for even stronger noise to incoherent firing leading to chaotic behavior of the excitable elements. For strong noise the system is less sensitive to the network topology. The specific topology enters via the degree of nodes and determines the average number of spikes. Apart from bifurcation regions, it is the ratio of noise intensity to size that determines the dynamical behavior of average values. Specific behavior such as limit cycles may then be realized for strong noise and large systems or for low noise and small systems. Within bifurcation regions, the actual values of noise intensity and system-size matter independently. Here we analyze in more detail phase portraits of small systems. For a given noise intensity and network topology we have studied the regularity of signals as a function of time. We observe the phenomenon of system-size resonance for a whole interval of noise intensities as long as the degree distribution is homogeneous, so that no fine tuning of the noise is needed. Therefore it is plausible that natural systems make actually use of noise when noise is unavoidably present.

Constructive Role of Internal Noise for the Detection of Weak Stimulation in a Coupled Biological Cell System

By constructing a mesoscopic stochastic model for intracellular calcium oscillations in coupled cell system, we investigated the influence of internal noise on the detection of weak stimulation using the chemical Langevin equation (CLE). We found that an optimal cell size V existed for a coupled cell chain length N and an optimal value of N existed for a given cell size V. At these values, the collective calcium oscillations showed the best performance, indicating the occurrence of"system size resonance (SSR)"or"internal noise stochastic resonance (INSR)". And such a phenomenon was robust to the coupling strength. Living cells may have learned to exploit the internal noise to detect weak stimulation via the mechanism of INSR, and then encode information to specifically regulate distinct cellular functions. It is interesting to note that the optimal cell size is always present at V≈103 μm3, which is close to the real living cell size in vivo. Since the internal noise in living systems can not be ignored and the systems may often encounter weak stimulations, our findings might have significance for stimulation detecting processes in living systems.

System Size Resonance Associated with Canard Phenomenon in a Biological Cell System

The influence of internal noise on the calcium oscillations is studied. It is found that stochastic calcium oscillations occur when the internal noise is considered, while the corresponding deterministic dynamics only yields a steady state. Also, the performance of such oscillations shows two maxima with the variation of the system size, indicating the occurrence of system size resonance. This behavior is found to be intimately connected with the canard phenomenon. Interestingly, it is also found that one of the optimal system sizes matches well with the real cell size, and such a match is robust to the variation of the control parameters.

System-size resonance for intracellular and intercellular calcium signaling

Dynamical behaviors of unidirectionally, linearly coupled as well as isolated calcium subsystems are investigated by taking into account the internal noise resulting from finite system size and thus small numbers of interacting molecules. For an isolated calcium system, the internal noise can induce stochastic oscillations for a steady state close to the Hopf-bifurcation point, and the regularity of those stochastic oscillations depends resonantly on the system size, exhibiting system-size resonance. For the coupled system consisting of two subsystems, the system-size resonance effect observed in the subsystem subject to coupling is significantly amplified due to the nontrivial effects of coupling.

Interacting stochastic oscillators

Stochastic coherence (SC) and self-induced stochastic resonance (SISR) are two distinct mechanisms of noise-induced coherent motion. For interacting SC and SISR oscillators, we find that whether or not phase synchronization is achieved depends sensitively on the coupling strength and noise intensities. Specifically, in the case of weak coupling, individual oscillators are insensitive to each other, whereas in the case of strong coupling, one fixed oscillator with optimal coherence can be entrained to the other, adjustable oscillator (i.e., its noise intensity is tunable), achieving phase-locking synchronization, as long as the tunable noise intensity is not beyond a threshold; such synchronization is lost otherwise. For an array lattice of SISR oscillators, except for coupling-enhanced coherence similar to that found in the case of coupled SC oscillators, there is an optimal network topology degree (i.e., number of coupled nodes), such that coherence and synchronization are optimally achieved, implying that the system-size resonance found in an ensemble of noise-driven bistable systems can occur in coupled SISR oscillators.

Neurodynamical amplification of perceptual signals via system-size resonance

We study the effect of finite-size synaptic noise on the response to time-varying stimuli of a detailed neurodynamical model of perceptual-decision making. Specifically, the reaction to a periodic stimulus is analyzed, while controlling the noise level through the number of neurons in the perception module. We find an enhanced response to the dynamical stimulus for intermediate noise, i.e. for an optimal system size. We thus propose a possible functional role of system-size resonance in a complex cognitive task.

Modulation on the collective response behavior by the system size in two-dimensional coupled cell systems

By the intracellular calcium ionic minimal model proposed by Berridge, we investigated the collective response of two-dimensional (N×N) coupled cell systems to the external stimulation using numerical simulation methods. With a coupled intensity fixed and an appropriate coupled cell number chosen, the kinetic system size resonance was discovered. At the same time, it was found that the system size responding to the external stimulation for different coupled intensities transferred too, especially when the coupled intensity increased, the range of the corresponding system size extended. These phenomena illustrate that the coupled cell number and the coupled intensity can play constructive roles in noisy coupled systems, by which the biology system would probably improve its capability to respond to the external stimulation.

System-Size Induced Coherence Resonance in Coupled MinimalCytosolic Ca2+ Oscillation Models

We have investigated the collective behaviour of an array of coupledminimal cytosolic Ca2+ oscillation models by numerical methods,taking into account the external noise resulting from the randomextracellular stimulation. It is found that the system size, i.e. thenumber of minimal cytosolic Ca2+ oscillation models, has anoptimal value, at which the system collective dynamics shows the bestperformance. The effect of the coupling strength has also been studied.Such a phenomenon of system-size resonance has been found for differentcoupling strengths, but the optimal system size increases when thecoupling strength increases.

Optimal observability of sustained stochastic competitive inhibition oscillations at organellar volumes

When molecules are present in small numbers, such as is frequently the case in cells, the usual assumptions leading to differential rate equations are invalid and it is necessary to use a stochastic description which takes into account the randomness of reactive encounters in solution. We display a very simple biochemical model, ordinary competitive inhibition with substrate inflow, which is only capable of damped oscillations in the deterministic mass-action rate equation limit, but which displays sustained oscillations in stochastic simulations. We define an observability parameter, which is essentially just the ratio of the amplitude of the oscillations to the mean value of the concentration. A maximum in the observability is seen as the volume is varied, a phenomenon we name system-size observability resonance by analogy with other types of stochastic resonance. For the parameters of this study, the maximum in the observability occurs at volumes similar to those of bacterial cells or of eukaryotic organelles.

System-size resonance in a binary attractor neural network

System size resonance (SSR) is a phenomenon in which the response of a system is optimal for a certain finite size, but poorer as the size goes to zero or infinity. In order to show SSR effects in binary attractor neural networks, we study the response of a network, in the ferromagnetic phase, to an external, time-dependent stimulus. Under the presence of such a stimulus, the network shows SSR, as is demonstrated by the measure of the signal amplification both analytically and by simulation.

Internal noise enhanced detection of hormonal signal through intracellular calcium oscillations

A variety of cell types respond to extracellular hormonal signals by repetitive intracellular calcium spikes. Here, by constructing a mesoscopic stochastic model for intracellular calcium oscillations in hepatocytes, we have investigated the influence of internal noise on the detection of sub-threshold hormonal signals using chemical Langevin equation (CLE) and Poisson approximation. It is found that stochastic calcium spikes appear when the internal noise is considered, and the regularity of the spike train undergoes a maximum with the variation of the internal noise level, indicating the occurrence of internal noise stochastic resonance (INSR). Since the magnitude of the internal noise is changed via the variation of the system size, the INSR also represents itself a kind of system size resonance.

Internal noise stochastic resonance of synthetic gene network

We have constructed a mesoscopic stochastic model for a synthetic gene network, and studied how the internal noise would influence the genetic oscillations of such a system. We find that the internal noise can play rather constructive roles via a mechanism of internal noise stochastic resonance, i.e., the stochastic genetic oscillations can show best performance at an optimal internal noise level. Since the magnitude of the internal noise is determined by the system size, this phenomenon also demonstrates a kind of system size resonance.