Nonlinear modelling of chemostat model with time delay and impulsive effect

In a neuronal system, propagation speed of neuronal information is mainly determined by the length, the diameter, and the kind of the axons between the neurons. Thus, some communications between neurons are not instantaneous, and others are instantaneous or with some negligible delay. In the past years, effects of time delay on neuronal dynamics, such as synchronization, stochastic resonance, firing regularity, etc., have been investigated. For stochastic resonance, it has been reported recently that stochastic multi-resonance in a neuronal system can be induced by time delay. However, in these studies, time delay has been introduced to every connection of the neuronal system. As mentioned in the beginning, in a real neuronal system, communication between some neurons can be instantaneous or with some negligible delays. Thus, considering the effect of partial time delay (time delay is called as partial time delay if only part of connections are delayed) on neuronal dynamics could be more meaningful.In this paper, we focus on discussing effect of partial time delay on response amplitude of a Watts-Strogatz neuronal network which is locally modeled by Rulkov map. With the numerically obtained results, we can see that partial time delay can induce a stochastic multi-resonance which is indicated by the multi-peak characteristics in the variation of response amplitude with partial time delay. Namely, partial time delay could also induce stochastic multi-resonance in a neuronal system. Moreover, we also find that optimal response amplitude can be reached in much wider range of the partial time delay value when delayed connections are less (i.e., the partial time delay probability is small). This is different from the case in which all connections are delayed, where response amplitude become optimal only when time delay is nearly the multiples of external signal's period. But the range of the partial time delay value becomes narrower and narrower with the increasing of the partial time delay probability and when the partial time delay probability is large enough, response amplitude becomes optimal only when time delay is nearly the multiples of external signal period. It is similar to the case where all connections are delayed. Furthermore, effects of random rewiring probability and total link number in the neuronal network on partial time delay induced stochastic multi-resonance are also studied. It is found that partial time delay induced stochastic multi-resonance is robust to random rewiring probability but not robust to total link number. Stochastic resonance is a very important nonlinear phenomenon in neuroscience, thus, our obtained results could have some implications in this field.

Finite-time synchronization of nonidentical BAM discontinuous fuzzy neural networks with delays and impulsive effects via non-chattering quantized control

The effect of pre-analytical handling on the stability of fractalkine, monocyte chemoattractant protein 1 (MCP1), interleukin 6 and interleukin 8 in samples of human cerebrospinal fluid

Imitation dynamics with time delay

Telementoring allows a less experienced surgeon to benefit from an expert surgical consultation, reducing cost, travel, and the learning curve associated with new procedures. However, there are several technical limitations that affect practical applications. One potentially serious problem is the time delay that occurs any time data are transferred across long distances. To date, the effect of time delay on surgical performance has not been studied. A two-phase trial was designed to examine the effect of time delay on surgical performance. In the first phase, a series of tasks was performed, and the numbers of robotic movements required for completion was counted. Programmed incremental time delays were made in audiovisual acquisition and robotic controls. The number of errors made while performing each task at various time delay intervals was noted. In the second phase, a remote surgeon in Baltimore performed the tasks 9000 miles away in Singapore. The number of errors made was recorded. As the time delay increased, the number of operator errors increased. The accuracy needed to perform remote robotic procedures was diminished as the time delay increased. A learning curve did exist for each task, but as the time delay interval increased, it took longer to complete the task. Time delay does affect surgical performance. There is an acceptable delay of <700 msec in which surgeons can compensate for this phenomenon. Clinical studies will be needed to evaluate the true impact of time delay.

A mathematical model describing continuous microbial culture and harvest in a chemostat, incorporating a control strategy and defined by impulsive differential equations, is presented and investigated. Theoretical results indicate that the model has a microbe-extinction periodic solution, which is globally attractive if the threshold R_{1} is less than unity, and the model is permanent if the threshold R_{2} is greater than unity. Further, we consider the control strategy under time delay and periodical impulsive effect. Analysis shows that continuous microbial culture and harvest process can be implemented by adjusting time delay, impulsive period or input amount of flocculant. Finally, we give an example with numerical simulations to illustrate the control strategy.

This study establishes a novel time-delay fractional SEIHR infectious disease model to investigate the effects of saturated incidence rates and time delays on different populations, including susceptibles, infected individuals, recovered individuals, and latent infected individuals. First, the existence and boundedness of the model’s solutions are verified, confirming its well-posedness. Subsequently, the existence of equilibria is analyzed, and the impact of parameter variations on the system is explored by examining the equilibria ϵ0 and ϵ∗, as well as the basic reproduction number R0. Additionally, the global dynamics of the equilibria are further analyzed using the Lyapunov method, while Hopf bifurcation theory is applied to explore the conditions under which the system shifts from stability to oscillatory behavior. Numerical simulations further validate the theoretical analysis, showing that time-delay effects significantly influence the system’s responsiveness and the rate of disease transmission. Moreover, when the time delay τ crosses the critical threshold τ0, the system exhibits periodic oscillations. By predicting periodic fluctuations and incorporating memory effects and persistent influences, we can better control epidemics, emphasizing the importance of time-delay adjustments and enhancing the system’s biological realism.

In this paper, based on inequality techniques and Lyapunov's second method, Global exponential stability (GES) problem of memristive complex-valued neural networks (MCVNNs) is discussed. The MCVNNs may be unstable due to time delay and impulsive effects. Therefore, we considered the influence of these two factors on the MCVNNs. For obtained the desire results we divide MCVNNs into two real-valued parts. Some new conditions are acquired to ensure the MCVNNs is stable. At the last, the simulations of real and imaginary parts are afforded to show the validity of the results by an example.

Effects of time delay on transient behavior of a time-delayed metastable system subjected to cross-correlated noises

With the rapid development of vehicular sensor networks (VSNs) technology, the potential use of networked real-time control and automation is enormous and appealing. However, closed-loop control VSNs via the Internet are very difficult to implement practically because of their stochastic nature. One of the biggest challenges in VSNs is how to deal with sensor networks time delay and data loss. The authors investigate the potential of using the predictive control scheme for VSNs based on round-trip time (RTT) delay prediction to overcome the VSNs transmission delay and data loss. The predicted RTT delay is taken as the sampling interval reference for variable-period sampling approach. Modelling the time delay of networked control systems as a non-linear time series, the least mean square (LMS) filter algorithm is adopted to predict online the time delay induced in VSNs. The simulation results show that the LMS algorithm can achieve ideal efficacy if time delay has no variety abnormally. The predictive compensation strategy is proposed to reduce the detrimental effect of stochastic time delays induced by communication networks on control performance. The results of offline simulations via the Internet illustrate that the predictive control scheme based on RTT delay prediction has the potential to overcome the VSNs time delay and data loss.

New discrete time domain models for the peak current controlled (PCC) power LED drivers in continuous conduction mode include for the first time the effects of the time delay in the pulse-width-modulator. Realistic amounts of time delay are found to have significant effects on the average output LED current and on the critical inductor value at the boundary between the two conduction modes. Especially, the time delay can provide an accurate LED current for the PCC buck converter with a wide input voltage. The models can also predict the critical inductor value at the mode boundary as functions of the input voltage and the time delay. The overshoot of the peak inductor current due to the time delay results in the increase of the average output current and the reduction of the critical inductor value at the mode boundary in all converters. Experimental results are presented for the PCC buck LED driver with constant-frequency controller.

Purpose– The purpose of this research is to explore the effect of time delay on the perception of environmental risks beyond time discounting, and thus provide a reference for effective communication related to environment and environmental risks.Design/methodology/approach– Ten risk scenarios across four time delay conditions were designed. Computer program randomly presented different risk scenarios to student subjects. Risk perception was measured through equivalent certain loss elicited by bi-section method. In all, 50 students from Harbin Institute of Technology Shenzhen Graduate School participated in the experiment.Findings– Time delay makes the subjects optimistic toward environmental risk with the exclusion of time discounting. The more distant in time the occurrence of an environmental risk, the less in intensity subjects will perceive it as a severe threat. Also, there is a noticeable difference in environmental risk perception between males and females.Research limitations/implications– This tentative research focusses on exploring the existence of time delay effect on environmental risk perception. Only student subjects are recruited for this research. Future studies are needed to extend the population to people of different backgrounds in order to generalize the finding.Practical implications– Current ethical appeal of zero social discount rate is unlikely to be effective. Time delay effect in people's environmental risk perception should be acknowledged. Such an acknowledgement is the basis of trust in risk communication. Communication effort needs to address this time delay effect to make people alert to long-term environmental risks, and eventually change their environmental behaviors.Originality/value– The explorative research represents the first attempt to investigate the effect of time delay on environmental risk perception when time discounting is excluded. It suggests a new direction to understand public optimism toward delayed environmental risks, and reluctance to take proactive actions, and thus offers a new insight into related communication efforts.

The dynamics of an age structured predator–prey model with disturbing pulse and time delays

This article is concerned with a generalized almost periodic multispecies mutualism model with impulsive effects and time delays. By utilizing comparison theorem and constructing a feasible Lyapunov function. We establish some criteria to guarantee that the permanence, existence, uniqueness and global stability of almost periodic positive solution. A feasible numerical simulation will be provided to explain the suitability of our main criteria.

The time-delayed feedback control for a supersonic airfoil results in interesting aeroelastic behaviors. The effect of time delay on the aeroelastic dynamics of a two-dimensional supersonic airfoil with a feedback control surface is investigated. Specifically, the case of a 3-dof system is considered in detail, where the structural nonlinearity is introduced in the mathematical model. The stability analysis is conducted for the linearized system. It is shown that there is a small parameter region for delay-independently stability of the system. Once the controlled system with time delay is not delay-independently stable, the system may undergo the stability switches with the variation of the time delay. The nonlinear aeroelastic system undergoes a sequence of Hopf bifurcations if the time delay passes the critical values. Using the normal form method and center manifold theory, the direction of the Hopf bifurcation and stability of Hopf-bifurcating periodic solutions are determined. Numerical simulations are performed to illustrate the obtained results.