Stochastic Time Delay Research Articles

Dynamics analysis of a delayed stochastic SIRS epidemic model with a nonlinear incidence rate

. This article proposes a stochastic delayed SIRS epidemic model with nonlinear incidence to describe disease transmission in a stochastic environment. First, it proves that the model has a unique global positive solution and derives sufficient conditions for the extinction and persistence of the epidemic in the population under appropriate conditions. Then, by constructing suitable Lyapunov functions, the asymptotic behavior of the model around the disease-free equilibrium and endemic equilibrium points of the deterministic model is analyzed, and it is concluded that under certain conditions, the solution of the stochastic system randomly oscillates around these two equilibrium points. Finally, several numerical examples are provided to validate the theoretical results, illustrating the significant impact of stochastic perturbations and time delays on disease control.

A novel kinetic model to demonstrate the independent effects of ATP and ADP/Pi concentrations on sarcomere function.

Understanding muscle contraction mechanisms is a standing challenge, and one of the approaches has been to create models of the sarcomere-the basic contractile unit of striated muscle. While these models have been successful in elucidating many aspects of muscle contraction, they fall short in explaining the energetics of functional phenomena, such as rigor, and in particular, their dependence on the concentrations of the biomolecules involved in the cross-bridge cycle. Our hypothesis posits that the stochastic time delay between ATP adsorption and ADP/Pi release in the cross-bridge cycle necessitates a modeling approach where the rates of these two reaction steps are controlled by two independent parts of the total free energy change of the hydrolysis reaction. To test this hypothesis, we built a two-filament, stochastic-mechanical half-sarcomere model that separates the energetic roles of ATP and ADP/Pi in the cross-bridge cycle's free energy landscape. Our results clearly demonstrate that there is a nontrivial dependence of the cross-bridge cycle's kinetics on the independent concentrations of ATP, ADP, and Pi. The simplicity of the proposed model allows for analytical solutions of the more basic systems, which provide novel insight into the dominant mechanisms driving some of the experimentally observed contractile phenomena.

Exponential mean‐square string stability of vehicular platoon with stochastic disturbance and time delay

AbstractPlatooning is an effective way to reduce air resistance and fuel consumption in vehicular transportation. However, stochastically generated disturbances can significantly impact the string stability of platoons. This article proposes a novel control law, based on sliding mode control and leader‐predecessor communications, designed to improve the exponential mean‐square string stability of platoons with Ito‐type stochastic disturbances that consider friction force. Specifically, our approach employs a third‐order nonlinear dynamic model to capture the relevant spatiotemporal correlations present in vehicle platoons. The proposed longitudinal control strategy effectively stabilizes the platoons with time delay and was verified through simulation experimentation. In this study, the stability of sliding mode motion is thoroughly investigated by means of sub‐reachable and practical stability analysis with sliding mode control. The findings of this study provide a theoretical foundation for further research on vehicle platoons with increasingly complicated interference and time delays. Overall, our results demonstrate that our approach can achieve significant improvements in both fuel economy and exhaust emissions while maintaining high levels of string stability, further contributing to the development of efficient and sustainable transportation systems.

An experimental and numerical study: to investigate the switching characteristics of a field-distortion sparkgap switch in various SF6 admixtures

Pressurized sparkgap switch is one of the major components that is most commonly used in various pulsed-power systems and the stochastic closure time delay (t d ) and jitter (σ d ) in this gas discharge switch has substantial effect on the temporal characteristics of output pulse. Experimental investigations performed with various volumetric concentrations of SF6 in SF6-N2, SF6-dry air and SF6-Ar admixtures evidenced that the intrinsic parameters of the switch such as time delay and jitter were found to be strongly dependent on the nature of gas, volumetric concentration of SF6 in admixture and rate of rise of voltage (dV/dT) of applied trigger pulse for e.g. in SF6/N2 admixture experiments as the concentration of SF6 was increased from 5% to 50% the average time delay and jitter was consequently increased from 278 ns to 413 ns and 17 ns to 56 ns, respectively. The similar increasing trend was observed even in SF6/dry air and SF6/Ar admixture experiments. It was also observed in the investigation that the variation in time delay and jitter is relatively much lesser for the condition when fast rising trigger pulse having slew rates ∼500 V ns−1 is applied than that of trigger pulse with lower dV/dT of ∼3 V ns−1. To further corroborate the stochasticity of streamer discharge in experimented SF6 admixtures, numerical studies have also been carried out by using a Particle-In-Cell/Monte Carlo Collision (PIC/MCC) model. Our experimental and simulation results infer that SF6/Ar admixture with low SF6 concentration is a superior alternative than pure SF6 for pulsed power switching applications.

Threshold dynamics and probability density functions of a stochastic predator–prey model with general distributed delay

Predator–prey interactions are among the most complicated interactions between biological species, in which there may be both delay digestion and stochastic fluctuation. In the literature, due to the computational complexity and the lack of available methods, few papers have directly considered the predator–prey model for the combination of general infinite time delays with stochasticity. In this sense, this work is devoted to studying the long-term qualitative behavior of a stochastic predator–prey system with general infinite distributed delay. First, we establish sufficient and necessary conditions for exponential extinction and persistence of species. Notably, not only do our results cover the predator–prey model without stochastic noises and time delays, but also reveal the impact of environmental noises on population dynamics. Moreover, there are some challenges to analyze the stationary distribution of the numbers of prey and predator under species persistence. Based on the recent work (Zhou et al., 2020) where the density function of a three-dimensional avian influenza model with non-degenerate diffusion is concerned, we further generalize the relevant theories to a five-dimensional population system with degenerate diffusion. Via solving the corresponding Fokker–Planck equations, several approximate expressions of the density function of the stochastic predator–prey system with special distribution delay kernels are obtained. Finally, we provide some numerical simulations to supplement the analytical results and study the impact of stochastic noises.

On exponential stability in [formula omitted]th moment of neutral Markov switched stochastic time-delay systems

In this article, the problem of the pth moment exponential stability is be investigated for neutral Markov switched stochastic time-delay systems. By virtue of inequalities based on the state-dependent multiple Lyapunov functions, we propose adequate conditions for the p-ES of Markov switched neutral stochastic differential delay equation applying properties for the stationary distribution of Markov switched process. For a class of neutral Markov switched stochastic time delay systems with impulse, several new criteria for pth moment exponential stability is obtained using the impulse average dwell-time condition, the integral transformation inequality, and stochastic analysis theory. The results extend and improve the related results from the existing literature. Some examples are provided to illustrate the validity of our derived results.

Aperiodic Event-Triggered Synchronization Control for Neural Networks With Stochastic Perturbations and Time Delay

In the presence of stochastic perturbations and time delay, the aperiodic event-triggered synchronization control for neural networks is studied in this paper. First, a suitable linear event-triggered control is designed to ensure the synchronization of the delayed stochastic neural networks in mean square. Then, by using Itô-differential formula, the synchronization criteria are derived under the event-triggered control. Moreover, a new method is proposed to prove that Zeno behavior does not occur, which ensures that the event-triggered control is feasible. Finally, an example and its simulation are provided to substantiate the effectiveness of the theory.

A new design method to global asymptotic stabilization of strict-feedforward stochastic nonlinear time delay systems

The stabilization problems of stochastic nonlinear systems remain challenging because many new obstacles will be encountered and need to be cautiously handled. This paper discusses the global asymptotic stabilization problem of stochastic nonlinear systems which possess strict-feedforward structure and multiple time delays. In the first place, we are trying to transform the considered system into an equivalent one by constructing the novel parameter-dependent state feedback controller and the suitable coordinate transformation. And then, through using the stochastic time delay system stability criterion and introducing the proper Lyapunov–Krasovskii functional, the global asymptotic stability of stochastic closed-loop system is proved. Finally, simulation results show the effectiveness of the parameter-dependent state feedback controller.

Memoryless parameter-dependent control strategy of stochastic strict-feedback time delay systems

For a class of stochastic strict-feedback nonlinear systems subject to different time delay states, this paper mainly concerns the problem of global asymptotic stabilization. Two new control strategies that the memoryless parameter-dependent state feedback control and the memoryless parameter-dependent output feedback control are taken into consideration, respectively. By skillfully constructing the Lyapunov-Krasovskii (L-K) functional, taking the proper determined parameter and employing the stochastic nonlinear time delay system (SNTDS) stability theory, the global asymptotic stability of the stochastic closed-loop system can be achieved. The proposed output feedback control scheme is finally utilized for the control design of the one-link manipulator system and two-stage chemical reactor system, which can verify the availability of the control approach.

Generic generation of noise-driven chaos in stochastic time delay systems: Bridging the gap with high-end simulations

Nonlinear time delay systems produce inherently delay-induced periodic oscillations, which are, however, too idealistic compared to observations. We exhibit a unified stochastic framework to systematically rectify such oscillations into oscillatory patterns with enriched temporal variabilities through generic, nonlinear responses to stochastic perturbations. Two paradigms of noise-driven chaos in high dimension are identified, fundamentally different from chaos triggered by parameter-space noise. Noteworthy is a low-dimensional stretch-and-fold mechanism, leading to stochastic strange attractors exhibiting horseshoe-like structures mirroring turbulent transport of passive tracers. The other is high-dimensional , with noise acting along the critical eigendirection and transmitted to "deeper" stable modes through nonlinearity, leading to stochastic attractors exhibiting swarm-like behaviors with power-law and scale break properties. The theory is applied to cloud delay models to parameterize missing physics such as intermittent rain and Lagrangian turbulent effects. The stochastically rectified model reproduces with fidelity complex temporal variabilities of open-cell oscillations exhibited by high-end cloud simulations.

Dynamics of a stochastic delayed chemostat model with nutrient storage and Lévy jumps

In this paper, a stochastic delayed chemostat model with nutrient storage and Lévy jumps is proposed. Firstly, the existence and uniqueness of the positive global solution of the model are discussed. Then, the threshold λ̄ and optimal control conditions for the persistence in the mean and extinction of the microorganism x are obtained. Besides, the ergodic stationary distribution of the SDDE model under a low-level intensity of stochastic noise is deduced. Finally, some numerical examples are given to support the theoretical analysis results. The simulation results show that stochastic noise and time delay play a vital role in controlling the persistence and extinction of microorganisms, respectively. On the one hand, high-intensity noise can inhibit the growth of microorganisms. On the other hand, if τ>τ∗, the corresponding deterministic model will become unstable and produce a Hopf bifurcation. Moreover, the solutions of the SDDE model will oscillate around the non-constant T−periodic solution of the corresponding deterministic model.

A simple stability criterion for dynamical systems with stochastic switching and/or stochastic time-delays

In many natural and technological systems the rule that governs the system’s dynamics changes over time. In such switched systems the system’s switching can be a significant source of instability. Here we give a simple sufficient criterium to determine if an i.i.d. stochastically switched system is stable in expectation. This method extends recent results for linear switched systems to nonlinear switched systems. It also extends results known for general switched systems giving improved results for systems with i.i.d. stochastic switching. The paper also considers the effects of time-delays on the stability of switched systems. Such time delays, which are intrinsic to any real-world system, can also have a destabilising effect on the system’s dynamics. Previously, it has been shown that if a dynamical system is intrinsically stable, which is a stronger form of global stability, then it maintains its stability even when time-delays are introduced into the system. Here we extend this notion to stochastically switched systems. We refer to this type of stability as patient stability and give a simple sufficient criterium under which such systems are patiently stable, i.e. cannot be destabilised by time delays. Both criteria introduced in this paper side step the need to use Lyapunov, linear matrix inequalities, and semi-definite programming-type methods. Our examples in this paper demonstrate the simplicity of these criteria.

Exacerbated drought accelerates catastrophic transitions of groundwater-dependent ecosystems in arid endorheic basins

• Two Haloxylon species exhibited distinct water use strategies but analogous bistable transitions. • Drought accelerates catastrophic shifts in both Haloxylon ecosystems by reducing resilience. • Natural and anthropogenic forcings are aggravating drought in groundwater-dependent ecosystems. • Drought adaptation strategies for such ecosystems must account for maintaining resilience. Drought has become a major threat to regional sustainable development in drylands. Ecological drought, emphasizing the process of drought impacts on ecosystems in coupled human-natural systems, has been posing large risks to the stability of groundwater-dependent ecosystems (GDEs) in drylands. Yet, the interconnected avenues via which ecological drought drives vegetation transition, ecological resilience and ecosystem services in GDEs with species-specific traits remain elusive, especially in arid endorheic basins. Here, we combine comprehensive field measurements derived from representative groundwater depth transects in Central Asia and simulations obtained from the stochastic eco-hydrological models and the Langevin approach, we find that two groundwater-dependent species, the salt-tolerant Haloxylon ammodendron and salt-sensitive Haloxylon persicum , exhibit contrasting water use strategies being driven by variations in eco-physiological traits and environmental regimes. Nonetheless, both the low-resilient H. ammodendron and high-resilient H. persicum vegetation tend to show bistable transition corresponding to vegetated and bare soils under drought stress with stochastic noises and time delays. Alarmingly, ecological drought is accelerating catastrophic transitions in both Haloxylon ecosystems induced by diminishing ecological flows, depleting soil moisture, and aggravating salinization, together with climate forcing. In particular, exacerbated drought stress reduces ecological resilience, enhances the likelihood of catastrophic shifts, and reduces ecosystem services of GDEs in arid endorheic basins. Our results highlight that ecological drought adaptation strategies must account for resilience maintenance by balancing water scarcity, water overuse, and water/soil quality to avoid accelerating regime shifts in dryland ecosystems.

Existence Uniqueness and Stability of Nonlocal Neutral Stochastic Differential Equations with Random Impulses and Poisson Jumps

This manuscript aims to investigate the existence, uniqueness, and stability of non-local random impulsiveneutral stochastic differential time delay equations (NRINSDEs) with Poisson jumps. First, we prove theexistence of mild solutions to this equation using the Banach fixed point theorem. Next, we prove thestability via continuous dependence initial value. Our study extends the work of Wang and Wu [15] wherethe time delay is addressed by the prescribed phase space B (defined in Section 3). An example is given toillustrate the theory.

Dynamics of a delayed stochastic epidemic model with double epidemic hypothesis and saturated incidence

This article explores a delayed stochastic epidemic model with double epidemic hypothesis and saturated incidence. First, we give some preliminaries of the epidemic system. Second, by building Lyapunov functions and utilizing inequalities, we study the asymptotic properties of the delayed stochastic system around each equilibrium point. Furthermore, we prove the persistence in mean of the epidemic system. In the end, several numerical simulations are presented to show that stochastic disturbance and time delay can impact the dynamics of the epidemic system.

Identifying partial topology of complex networks with stochastic perturbations and time delay

In various practical scenarios, the topology of a complex network is generally unknown or unavailable. Based on the adaptive feedback control strategy and the pining mechanism, some controllers and observers are designed in this manuscript to identify the partial topology of the noise-contaminated networks with coupling delay. The approach can be extended to infer the whole topology of the networks. For large-scale complex networks, our approach greatly reduces the calculation compared with the previous methods. Numerical simulations are employed to illustrate the effectiveness of the proposed theoretical results.

Active vibration on offshore steel jacket platforms including delayed probabilistic actuator failures and resilient reliable sampled‐data control

This paper examines the unified dissipative performance of Offshore Steel Jacket Platforms (OSJPs) which include actuator failures and probabilistic delays, through a resilient and reliable sampled-data controller. In detail, random variables fetching the Bernoulli distribution are treated in particular for the stochastic time-delays. By implementing the Lyapunov–Krasovskii functions(LKF) together with the Second Order Bessel–Legendre Inequality Technique (SOBLIT) and an improved Reciprocally Convex Inequality (RCI) approach, which provides impressive information about sampling to guarantee that the OSJP is unified dissipative. The proposed criterion is exhibited in the sort of linear matrix inequalities (LMIs) and highlights of this study is to examine the multi-dynamic interpretation of OSJP with extended dissipativity indices. The advantage of the established methodology is explored for OSJPs with the existing results, which is carried out along with the proposed control law, using their values of the experimental parameters.

Retraction: State estimation of Takagi‐Sugeno fuzzy system in networked control system with stochastic time delays under unknown attacks

International Journal of Adaptive Control and Signal ProcessingVolume 36, Issue 8 p. 2150-2150 RETRACTION STATEMENTFree Access Retraction: State estimation of Takagi-Sugeno fuzzy system in networked control system with stochastic time delays under unknown attacks This article retracts the following: Retracted: State estimation of Takagi-Sugeno fuzzy system in networked control system with stochastic time delays under unknown attacks Muhammad Shamrooz Aslam, Volume 35Issue 7International Journal of Adaptive Control and Signal Processing pages: 1336-1353 First Published online: June 22, 2021 First published: 13 July 2022 https://doi.org/10.1002/acs.3469AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat The above article from the International Journal of Adaptive Control and Signal Processing, published online on June 22, 2021 in Wiley Online Library (http://onlinelibrary.wiley.com/), has been retracted by agreement between the journal Editor in Chief, Professor Mike Grimble, and John Wiley and Sons Ltd. The retraction has been agreed due to unattributed overlap between this article and the following article submitted to IEEE Transactions on Fuzzy Systems: “Event-triggered fault detection filter design for networked switched T-S fuzzy systems with deception attacks and data disorders (TFS-2019-1136)”. Authors: Qi, Yiwen; Yuan, Shuo; Zhao, Xudong. Submitted Nov 2019. REFERENCE 1Aslam, MS. State estimation of Takagi-Sugeno fuzzy system in networked control system with stochastic time delays under unknown attacks. Int J Adapt Control Signal Process 2021; 35: 1336– 1353. https://doi.org/10.1002/acs.3241 Volume36, Issue8August 2022Pages 2150-2150 ReferencesRelatedInformation

Stability and synchronization for complex-valued neural networks with stochastic parameters and mixed time delays.

In this paper, a class of complex-valued neural networks (CVNNs) with stochastic parameters and mixed time delays are proposed. The random fluctuation of system parameters is considered in order to describe the implementation of CVNNs more practically. Mixed time delays including distributed delays and time-varying delays are also taken into account in order to reflect the influence of network loads and communication constraints. Firstly, the stability problem is investigated for the CVNNs. In virtue of Lyapunov stability theory, a sufficient condition is deduced to ensure that CVNNs are asymptotically stable in the mean square. Then, for an array of coupled identical CVNNs with stochastic parameters and mixed time delays, synchronization issue is investigated. A set of matrix inequalities are obtained by using Lyapunov stability theory and Kronecker product and if these matrix inequalities are feasible, the addressed CVNNs are synchronized. Finally, the effectiveness of the obtained theoretical results is demonstrated by two numerical examples.

A fully probabilistic control framework for stochastic systems with input and state delay

This paper proposes a unified probabilistic control framework for a class of stochastic systems with both control input and state time delays. Both of the stochastic nature and time delays in the system dynamics are considered simultaneously, thus providing a comprehensive and rigorous control methodology. The problem is formulated in a fully probabilistic framework, where the system dynamics and its controller are fully characterised by arbitrary probabilistic models. In this framework, the Kullback–Leibler Divergence between the actual joint probability density function of the system dynamics and controller and a predefined ideal joint probability density function is used to characterise the discrepancy between the two distributions and derive the randomised controller. Time delays in the control input and system state are taken into consideration in the optimisation process for the derivation of the optimal randomised controller. Besides, the analytic control solution of the time delay fully probabilistic control problem for a class of linear Gaussian stochastic systems is derived while the successive approximation approach is implemented to deal with the time-advanced components in the control law that result from the existence of time delays. The effectiveness of the proposed control framework is then illustrated on a numerical example and a real-world example.