Stochastic synchronization via noise recycling

Effect of internal and external chaotic stimuli on synchronization of piezoelectric auditory neurons in coupled time-delay systems

Hearing impairment is considered to be related to the damage of hair cells or synaptic terminals, which will cause varying degrees of hearing loss. Numerous studies have shown that cochlear implants can balance this damage. The human ear receives external acoustic signals mostly under complex conditions, and its biophysical mechanisms have important significance for reference in the design of cochlear implants. However, the relevant biophysical mechanisms have not yet been fully determined. Using the characteristics of special acoustoelectric conversion in piezoelectric ceramics, this paper integrates them into the traditional FitzHugh-Nagumo neuron circuit and proposes a comprehensive model with coupled auditory neurons. The model comprehensively considers the effects of synaptic coupling between neurons, information transmission delay, external noise stimulation, and internal chaotic current stimulation on the synchronization of membrane potential signals of two auditory neurons. The experimental results show that coupling strength, delay size, noise intensity, and chaotic current intensity all have a certain regulatory effect on synchronization stability. In particular, when auditory neurons are in a chaotic state, their impact on synchronization stability is sensitive. Numerical results provide a reference for exploring the biophysical mechanisms of auditory neurons. At the same time, we are committed to providing assistance in using sensors to monitor signals and repair hearing impairments.

Effects of chaotic activity and time delay on signal transmission in FitzHugh-Nagumo neuronal system

The influences of chaotic activity and time delay on the transmission of the sub-threshold signal (STS) in a single FitzHugh-Nagumo neuron and coupled neuronal networks are studied. It is found that a moderate chaotic activity level can enhance the system's detection and transmission of STS. This phenomenon is known as chaotic resonance (CR). In a single neuron, the large amplitude and small period of the STS have a positive effect on the CR phenomenon. In the coupled neuronal network, however, the signal transmission performance of chemical synapses is better than that of electrical synapses. The time delay can determine the trend of the system response, and the multiple chaotic resonances phenomenon is observed upon fine-tuning the time delay length. Both sub-harmonic chaotic resonance and chaotic anti-resonance appear when the STS period and time delay are locked. In chained networks, the signal transmission performance between electrical synapses attenuates continuously. Conversely, the performance between chemical synapses reaches a steady state.

Logical response induced by temperature asymmetry

It is known that the reliable logical response can be extracted from a noisy bistable system at an intermediate value of noise strength when two random or periodic, two-level, square waveform serve as the inputs. The asymmetry of the potential has a very important role and dictates the type of logical operation, such as or or and, exhibited by the system. Here we show that one can construct logic gates with symmetric bistable potential if the two states of the double-well are thermalized with two different heat baths. It has been found that if a given state is kept at a sufficiently low temperature compared to the other, the system shows one kind of logic behavior (say, or). Interestingly, the system's response turns into the other kind (say, and) if the temperature of the initial low-temperature well is increased gradually and the quality of the logical response first improves and then weakens after passing through a maximum at a particular value. However, the reliability of the second kind of logical response (and) is not as good as the first kind (or) and depends on the amplitude of the inputs. Still one can construct both kinds of logic gates with maximum reliability by properly choosing the initial low-temperature well.

Stochastic resonance in a delayed triple-well potential driven by correlated noises

In this paper, we investigate stochastic resonance (SR) in a delayed triple-well potential subject to correlated noises and a harmonic signal. The stationary probability density, together with the response amplitude of the system, is obtained by using the small time delay approximation. It is found that the time delay, noise intensities, and the cross-correlation between noises can induce the occurrence of the transition. Moreover, the appropriate choice of noise intensities and time delay can improve the output of the system, enhance the SR effect, and lead to the phenomenon of noise enhanced stability. Especially, the stochastic multi-resonance phenomenon is observed when the multiplicative and additive noises are correlated. Finally, the theoretical results are well verified through numerical simulations.

Modulating resonance behaviors by noise recycling in bistable systems with time delay

In this paper, the impact of noise recycling on resonance behaviors is studied theoretically and numerically in a prototypical bistable system with delayed feedback. According to the interior cooperating and interacting activity of noise recycling, a theory has been proposed by reducing the non-Markovian problem into a two-state model, wherein both the master equation and the transition rates depend on not only the current state but also the earlier two states due to the recycling lag and the feedback delay. By virtue of this theory, the formulae of the power spectrum density and the linear response function have been found analytically. And the theoretical results are well verified by numerical simulations. It has been demonstrated that both the recycling lag and the feedback delay play a crucial role in the resonance behaviors. In addition, the results also suggest an alternative scheme to modulate or control the coherence or stochastic resonance in bistable systems with time delay.

Resonance dynamics evoked via noise recycling procedure

We study the effect of noise recycling on nonequilibrium escape dynamics in a bistable system. For small noise, the non-Markovian problem is reduced to a two-state model with the master equation depending on not only the current state but also the earlier state, based on which we are able to derive the analytical formulas for the switching rate, the autocorrelation function, and the power spectrum density (PSD). Both the theoretical and the numerical results show that, with modulating the time delay in noise recycling, a monotonic PSD may switch to a nonmonotonic one; the amplitude of PSD at resonance frequency exhibits a pronounced maximum at a certain noise level, declaring the onset of stochastic resonance (SR) in the absence of a weak periodic signal. Further, we also demonstrate that the linear response to the external periodic force displays a maximum at a certain level of time delay, displaying the signature of SR.

Logical stochastic resonance with correlated internal and external noises in a synthetic biological logic block

Following the advent of synthetic biology, several gene networks have been engineered to emulate digital devices, with the ability to program cells for different applications. In this work, we adapt the concept of logical stochastic resonance to a synthetic gene network derived from a bacteriophage λ. The intriguing results of this study show that it is possible to build a biological logic block that can emulate or switch from the AND to the OR gate functionalities through externally tuning the system parameters. Moreover, this behavior and the robustness of the logic gate are underpinned by the presence of an optimal amount of random fluctuations. We extend our earlier work in this field, by taking into account the effects of correlated external (additive) and internal (multiplicative or state-dependent) noise. Results obtained through analytical calculations as well as numerical simulations are presented.

Phase induced transport of a Brownian particle in a periodic potential in the presence of an external noise: A semiclassical treatment

We develop, invoking a suitable system-reservoir model, the Langevin equation with a state-dependent dissipation associated with a quantum Brownian particle submerged in a heat bath that offers a state-dependent friction to study the directed motion (by studying the phase-induced current) in the presence of an external noise. We study the phase induced current when both system and bath are subjected to external modulation by the noise and thereby expose the system to two cross-correlated noises. We also demonstrate the well-known fact that two noises remain mutually correlated if they share a common origin. We study the effects of correlation on the current in a periodic potential and envisage that the steady state current increases with increase in the extent of correlation, implying that exercising control on the degree of correlation can enhance the current in a properly designed experiment. To establish our model, we analyze numerically the effect of the external noise on system and bath separately as well as on composition of both.