Narrow Results

The RR and RT time intervals extracted from the electrocardiogram measure respectively the duration of cardiac cycle and repolarization. The series of these intervals recorded during the exercise test are characterized by two trends: A decreasing one during the stress phase and an increasing one during the recovery, separated by a global minimum. We model these series as a sum of a deterministic trend and random fluctuations, and estimate the trend using methods of curve extraction: Running mean, polynomial fit, multi scale wavelet decomposition. We estimate the minimum location from the trend. Data analysis performed on a group of 20 healthy subjects provides evidence that the minimum of the RR series precedes the minimum of the RT series, with a time delay of about 19 seconds.

The phenomenon of stochastic resonance in a bacterium growth system that is with two different kinds of time delays and is driven by colored noises is investigated. Based on the extended unified colored noise theory and the method of the probability density approximation, the Fokker–Planck equation and the stationary probability density function are derived. Then via the theory of adiabatic limit, the analytical expression of the signal-to-noise ratio (SNR) is obtained. The different effects of the time delays existed in the nonlinear system and the noise correlation times on the stationary probability density and the signal-to-noise rate are discussed respectively. Finally, numerical simulations are offered and are consistent with approximate analytical results.

In this paper, the stability and the phenomenon of stochastic resonance (SR) for a stochastic time-delayed cancer development system that is induced by the multiplicative periodic signal, the multiplicative and the additive noises are investigated. By using the fast descent method, small time delay method and the two-state theory, the expressions of the steady state probability distribution function and the signal-to-noise ratio (SNR) are obtained. Numerical results reflect that the multiplicative and additive noise always restrain the diffusion of the cancer cells. Whereas, the time delay can not only control the spread of the tumor cells, but also suppress the extinction of cancer cells. Meanwhile, the conventional SR occurs in the tumor cell growth model under the excitation of different noises and time delay. In conclusion, the multiplicative noise always plays a critical role in restraining SR, a smaller additive noise can stimulate the SR, but the larger additive noise can weaken the SR and SNR. In particular, the time delay displays relatively complicated effects on the SR phenomenon of the system. It plays different roles in motivating or suppressing SR under the different conditions of parameters.

In this paper, we study the effect of channel noise on the temporal coherence of scale-free Hodgkin–Huxley neuronal networks with time delay. It is found that the temporal coherence of the neuronal networks changes as channel noise intensity is varied in different ways depending on the range of channel noise intensity. The temporal coherence monotonically decreases with the increase of channel noise intensity for too small or too big channel noise intensity. However, for intermediate channel noise intensity it intermittently and rapidly becomes high and low as channel noise intensity is varied, exhibiting temporal coherence transitions. Moreover, this phenomenon is dependent on coupling strength and network average degree and becomes strongest when they are optimal. This result shows that channel noise has a regulation effect on the temporal coherence of the delayed neuronal networks by inducing temporal coherence transitions. This provides a new insight into channel noise for the information processing and transmission in neural systems.

In this paper, we numerically study the effect of channel noise on synchronization transitions induced by time delay in adaptive scale-free Hodgkin–Huxley neuronal networks with spike-timing-dependent plasticity (STDP). It is found that synchronization transitions by time delay vary as channel noise intensity is changed and become most pronounced when channel noise intensity is optimal. This phenomenon depends on STDP and network average degree, and it can be either enhanced or suppressed as network average degree increases depending on channel noise intensity. These results show that there are optimal channel noise and network average degree that can enhance the synchronization transitions by time delay in the adaptive neuronal networks. These findings could be helpful for better understanding of the regulation effect of channel noise on synchronization of neuronal networks. They could find potential implications for information transmission in neural systems.

In this paper, our aim is to investigate the steady state behaviors, the stochastic resonance (SR) phenomenon and the mean decline time for a biological insect growth system induced by the terms of time delay, the multiplicative and additive noises. Numerical results indicate that the multiplicative noise and the additive one can both weaken the stability of the biological system and accelerate the depression process of the insect population, while time delay can strengthen the stability of the insect growth system and prolong the lifetime of the insect system. With respect to the SR phenomenon caused by time delay, noise terms and the weak periodic signal, the results show that some interesting dual peak phenomena for the signal-to-noise ratio (SNR) occur frequently. Specific contents are as follows: In SNR-$Q$ plots, the additive noise intensity $M$ and time delay $\tau$ can easily induce the phenomenon of dual peaks, while in the SNR-$M$ plots, the multiplicative noise intensity $Q$ and time delay $\tau$ can both reduce the SR effect distinctly. On the other hand, in the SNR-$\tau$ plots, when either of $Q$ or $M$ takes a big value, the other plays a negative role in stimulating the SR phenomenon; while either of them takes a small value, the other can excite a significant effect of double peaks.

In this paper, we study effect of channel block (CB) on multiple coherence resonance (MCR) in adaptive scale-free Hodgkin–Huxley neuronal networks with spike-timing-dependent plasticity (STDP). It is found that potassium CB suppresses MCR, but sodium CB can enhance MCR, and there is optimal sodium CB level by which MCR becomes most pronounced. In addition, STDP has a significant influence on the effect of CB on MCR. As adjusting rate $A_p$ of STDP increases, for potassium CB there is proper $A_p$ by which MCR is most pronounced; however, for sodium CB MCR is reduced. These findings could provide a new insight into effect of CB on information processing in neural systems.

In the present paper, the stability of the population system and the phenomena of the stochastic resonance (SR) for a metapopulation system induced by the terms of time delay, the multiplicative non-Gaussian noise, the additive colored Gaussian noise and a multiplicative periodic signal are investigated in detail. By applying the fast descent method, the unified colored noise approximation and the SR theory, the expressions of the steady-state probability function and the SNR are derived. It is shown that multiplicative non-Gaussian noise, the additive Gaussian noise and time delay can all weaken the stability of the population system, and even result in population extinction. Conversely, the two noise correlation times can both strengthen the stability of the biological system and contribute to group survival. In regard to the SNR for the metapopulation system impacted by the noise terms and time delay, it is revealed that the correlation time of the multiplicative noise can improve effectively the SR effect, while time delay would all along restrain the SR phenomena. On the other hand, although the additive noise and its correlation time can stimulate easily the SR effect, they cannot change the maximum of the SNR. In addition, the departure parameter from the Gaussian noise and the multiplicative noise play the opposite roles in motivating the SR effect in different cases.

In the present paper, the stability and the phenomena of stochastic resonance (SR) for a FitzHugh–Nagumo (FHN) system with time delay driven by a multiplicative non-Gaussian noise and an additive Gaussian white noise are investigated. By using the fast descent method, unified colored noise approximation and the two-state theory for the SR, the expressions for the stationary probability density function (SPDF) and the signal-to-noise ratio (SNR) are obtained. The research results show that the two noise intensities and time delay can always decrease the probability density at the two stable states and impair the stability of the neural system; while the noise correlation time $\tau$ can increase the probability density around both stable states and consolidate the stability of the neural system. Furthermore, the other noise correlation time ${\tau }_0$ can increase the probability at the resting state, but reduce that around the excited state. With respect to the SNR, it is discovered that the two noise strengths can both weaken the SR effect, while time delay $\alpha$ and the departure parameter $q$ will always amplify the SR phenomenon. Moreover, the noise correlation time ${\tau }_0$ can motivate the SR effect, but not alter the peak value of the SNR. What’s most interesting is that the other noise correlation time $\tau$ can not only stimulate the SR phenomenon, but also results in the occurrence of two resonant peaks, whose heights are simultaneously improved because of the action of $\tau$.

In this paper, the regime shift behaviors between the prosperous state and the extinction state and stochastic resonance (SR) phenomenon for a metapopulation system subjected to time delay and correlated Gaussian colored noises are investigated. Through the numerical calculation of the modified potential function and the stationary probability density function (SPDF), one can make clearly the following results: Both multiplicative noise and noise correlation times can improve effectively the ecological stability and prolong the survival time of the system; while additive noise, time delay and noise correlation strength can weaken significantly the biological stability and speed up the extinction of the population. As for the signal-to-noise ratio (SNR), it is found that time delay, multiplicative noise and noise correlation strength can all impair the SR effect. Conversely, the two noise correlation times and additive noise are in favor of the improvement of the peak values of SNR. It is particularly worth mentioning that in the case of $M=0.03$, time delay $\alpha$ and self-correlation time ${\tau }_2$ of the additive noise display exactly the opposite effect on the stimulation of the resonant peak in the SNR–$\lambda$ plots.

This paper deals with the problem of mixed $H_{\infty }$ and passivity performance analysis of digital filters subject to Markovian jumping parameters, external disturbances, time delays and bounds of the nonlinearity functions. By employing Lyapunov theory and matrix decomposition technique, a novel sufficient condition is established. The proposed criterion ensures that the underlying system is stochastically stable and satisfies a mixed $H_{\infty }$ and passivity performance index simultaneously. The obtained criterion can also be employed to solve the $H_{\infty }$ problem or the passivity problem in a unified framework. Moreover, the problem is formulated to obtain optimal mixed $H_{\infty }$ and passivity performance index of the interfered digital filters. The effectiveness and superiority of our proposed results are illustrated by three examples.

In this paper, we focus on the investigations on the stochastic stability and the stochastic resonance (SR) phenomena for a FitzHugh-Nagumo system with time delay induced by a multiplicative non-Gaussian colored noise and an additive Gaussian colored noise. By use of the fast descent method, the unified colored noise approximation and the two-state theory for the SR, the stationary probability density function (SPDF) and the signal-to-noise ratio (SNR) caused by different noise terms and time delay are explored. The investigation results indicate that the two noise intensities, time delay and the departure parameter from the Gaussian noise can all reduce the probability density around the two stable states and destroy the stability of the neural system; while the two noise correlation times $\tau$ and ${\tau }_0$ can both improve the probability density around both stable states and reinforce the biological stability of the neural system. As regards the SNR, it is found that the two noise intensities and the departure coefficient can all weaken the SR effect, while time delay $\alpha$ and the correlation time $\tau$ of the multiplicative noise will always magnify the SR phenomenon. It is worth to mention that the correlation time ${\tau }_0$ of the additive noise can stimulate the SR effect, but not alter the maximum of the SNR.

In this paper, we establish a stochastic dynamical grazing ecosystem with time delays and fluctuations. The effects of time delay, Gaussian noise and Lévy noise on the stationary probability distribution (SPD), the mean first passage time (MFPT) and stochastic resonance (SR) are analyzed. Our research results show the following: (i) For small time delay, the increasing Gaussian noise intensity leads to catastrophic regime shift (CRS) from high vegetation state to low vegetation state, while the increasing Lévy noise intensity contributes to the recovery of these shifts. For large time delay, the increasing Gaussian noise intensity or Lévy noise intensity causes the CRS phenomenon, the larger the time delay, the more frequent the CRS phenomenon. (ii) The increasing Gaussian noise intensity can diminish the stability of the high vegetation state and low vegetation state, the increasing Lévy noise intensity and Lévy stability index can enhance the stability of the high vegetation state and diminish the stability of the low vegetation state. The increasing Lévy noise intensity can lead to noise-enhanced stability (NES) of the high vegetation state, and the larger the time delay, the more pronounced the NES phenomenon. (iii) The increase of time delay can weaken SR phenomenon when signal-to-noise ratio (SNR) is a function of Gaussian noise intensity and Lévy noise intensity.