Synchronization control of stochastic delayed Lotka\u2013Volterra systems with hardware simulation

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.

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

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.

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 order to study the impact of random environments during the spread of the disease, we propose a novel stochastic SIQS model on scale-free networks, which introduces stochastic perturbations to the infected rates. We first obtain the existence of global positive solutions. Moreover, by constructing appropriate stochastic Lyapunov functions, we prove sufficient conditions for extinction and persistence of the disease. Finally, we verify the analysis results through numerical simulations. In addition, the results of previous studies are also improved in our research.

Considering the influences of uncertain factors on the reproduction of virus in vivo, a stochastic HIV model with CTLs’ immune response and logistic growth was developed to research the dynamics of HIV, where uncertain factors are white noise and telegraph noise. which are described by Brownian motion and Markovian switching, respectively. We show, firstly, the existence of global positive solutions of this model. Further, by constructing suitable stochastic Lyapunov functions with regime switching, some sufficient conditions for the existence and uniqueness of the stationary distribution and the conditions for extinction are obtained. Finally, the main results are explained by some numerical examples. Theoretical analysis and numerical simulation show that low-intensity white noise can maintain the persistence of the virus, and high intensity white noise can make the virus extinct after a period of time with multi-states.

This paper is concerned with a delay logistical model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall′s inequality, and Young′s inequality, some sufficient conditions for existence of global positive solutions and stochastically ultimate boundedness are obtained, respectively. Also, the relationships between the stochastic permanence and extinction as well as asymptotic estimations of solutions are investigated by virtue of V‐function technique, M‐matrix method, and Chebyshev′s inequality. Finally, an example is given to illustrate the main results.

A modified stochastic ratio‐dependent Leslie‐Gower predator‐prey model is formulated and analyzed. For the deterministic model, we focus on the existence of equilibria, local, and global stability; for the stochastic model, by applying Itô formula and constructing Lyapunov functions, some qualitative properties are given, such as the existence of global positive solutions, stochastic boundedness, and the global asymptotic stability. Based on these results, we perform a series of numerical simulations and make a comparative analysis of the stability of the model system within deterministic and stochastic environments.

Asymptotic properties of a stochastic Gilpin–Ayala model under regime switching

We present and analyze a modified Holling type-II predator-prey model that includes some important factors such as Allee effect, density-dependence, and environmental noise. By constructing suitable Lyapunov functions and applying Itô formula, some qualitative properties are given, such as the existence of global positive solutions, stochastic boundedness, and the global asymptotic stability. A series of numerical simulations to illustrate these mathematical findings are presented.

This paper is concerned with a stochastic nonautonomous logistic model with jumps. In the model, the martingale and jump noise are taken into account. This model is new and more feasible and applicable. Sufficient criteria for the existence of global positive solutions are obtained; then asymptotic boundedness inpth moment, stochastically ultimate boundedness, and asymptotic pathwise behavior are to be considered.

Closed-loop identification with routine operating data: Effect of time delay and sampling time

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

McDonnell Douglas Helicopter Company recently undertook a study to determine the actual simulator hardware time delay in all the simulators, It also investigated the effect of time delay on pilot performance and his aircraft evaluaiion in- an engineering design environment. This paper describes the system architecture, techniques -of measuring thruput delays, and initial study results. It was found that the average total system delay was about 87 milliseconds, well below values reported in open literature for most of the training and engineering simulators. The second phase of the study involved systematically varying the simulator delays so that data on the effect of time delay could be collected and used as a useful parameter in aircraft /simulator design. Pilot performance was recorded and subjective evalua- tions in the form of Cooper-Harper ratings were also obtained. Analysis of pilot performance did not provide any dramatic changes due to increased simulator delays but did show that the pilot control activity increased in the low speed, high gain tasks. It was found that with increased time delay the Cooper-Harper rating increased indicating degradation in perceived handling qualities. However, for the type of helicopter simulated, there was not a definite time delay at which the ratings changed abruptly. This indicates that for engineering design purposes while it is desirable to keep the delay to the absolute minimum, there may be sufficient flexibil- ity in the design of the simulator to permit cost/ capability trade offs. However, this needs to be further validated by additional tests that introduce pilot dis- tractions (such as gusts) and force the pilot to increase his closed loop gain. Abbreviations

Anaerobic digestion of municipal and animal wastes provides a potentially important means of producing energy sustainably. The reliable production of methane from anaerobic digestion requires that bacteria metabolise municipal and agricultural wastes to produce mainly carbon dioxide and methane. Our model uses Monod based kinetics and is complex since the biomass concentration growth is inhibited with the increase in substrate. The production of methane depends on the number of methanogenic bacteria; there is evidence from previous chemostats experiments that there is a time delay in population number of these cells to respond to changes in substrate concentrations. In this article we focus on determining the dynamical response of the methane production rate under different dynamics of feed conditions and temperatures. Since there is a delay in the methane bacteria mass response, we include the effects of the delay on the dynamics of the system based on modification of kinetics in a simple fermentation anaerobic model. We compare the dynamics of the system with and without delay to show the contribution of delay to the overall stability of the system. References O. Bernard, Z. Hadj-Sadok, D. Dochain, A. Genovesi, J. P. Steyer. Dynamical model development and parameter identification for an anaerobic wastewater treament process. Biotechnol. Bioeng. 75:424–438, 2001. doi:10.1002/bit.10036 T. F. Thingstad and T. I. Langeland. Dynamics of chemostat culture: The effect of a delay in cell response. J. Theor. Biol. , 48:149–159, 1974. doi:10.1016/0022-5193(74)90186-6 J. R. Beddington and R. M. May. Time delays are not nessarily destabilizing. Math. Biosci. 27:109–119, 1975. doi:10.1016/0025-5564(75)90028-0 K. Y. San and G. Stephanopoulos. The effect of growth rate delays in substrate-inhibited kinetics on the optimal profile of fed-batch reactors. J. Theor. Biol. 28:356–361, 1986. doi:10.1002/bit.260280308 G. Stephanopoulos and K. Y. San. Studies on-line bioreactor identification. I. Theory. Biotechnol. Bioeng. 26:1176–1188, 1984. doi:10.1002/bit.260261006 A. A. Khan, A. J. Stacey and J. J. Shepherd. Optimization of methane output for an anaerobic waste digester. ANZIAM J. 54:C523–C539, 2013. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/6322 J. F. Andrews. A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates. Biotechnol. Bioeng. 10:707–723, 1968. doi:10.1002/bit.260100602 D. J. Batstone, J. Keller, I. Angelidaki, S. V. Kalyuzzhni, S. G. Pavlostathis, A. Rozzi, W. T. M. Sanders, H. Siegrist, and V. A. Vavilin. Anaerobic digestion model No. 1 (ADM1). Water Sci. Technol. 45(10):65–73, 2002 http://wst.iwaponline.com/content/45/10/65 K. J. Beers. Numerical methods for chemical engineering: Applications in Matlab . Cambridge, New York, USA, 2007. http://www.cambridge.org/us/academic/subjects/engineering/chemical-engineering/numerical-methods-chemical-engineering-applications-matlab J. F. Andrews. The development of a dynamic model and control strategies for the anaerobic digestion process. In Mathematical Models in Water Pollution Control , A. James (ed). Wiley, 1978. A. W. Bush and A. E. Cook. The effect of time delay and growth rate inhibition in the bacterial treatment of wastewater J. Theor. Biol. 63:385–395, 1976. doi:10.1016/0022-5193(76)90041-2 L. F. Shampine, I. Gladwell and S. Thompson. Solving ODEs with Matlab . Cambridge, New York, USA, 2003. http://www.cambridge.org/us/academic/subjects/mathematics/numerical-analysis/solving-odes-matlab?format=PB