Critical Time Delay Research Articles

Delay-driven phase transitions in an epidemic model on time-varying networks.

A complex networked system typically has a time-varying nature in interactions among its components, which is intrinsically complicated and therefore technically challenging for analysis and control. This paper investigates an epidemic process on a time-varying network with a time delay. First, an averaging theorem is established to approximate the delayed time-varying system using autonomous differential equations for the analysis of system evolution. On this basis, the critical time delay is determined, across which the endemic equilibrium becomes unstable and a phase transition to oscillation in time via Hopf bifurcation will appear. Then, numerical examples are examined, including a periodically time-varying network, a blinking network, and a quasi-periodically time-varying network, which are simulated to verify the theoretical results. Further, it is demonstrated that the existence of time delay can extend the network frequency range to generate Turing patterns, showing a facilitating effect on phase transitions.

Dynamics of a diffusive model for cancer stem cells with time delay in microRNA-differentiated cancer cell interactions and radiotherapy effects

Understand the dynamics of cancer stem cells (CSCs), prevent the non-recurrence of cancers and develop therapeutic strategies to destroy both cancer cells and CSCs remain a challenge topic. In this paper, we study both analytically and numerically the dynamics of CSCs under radiotherapy effects. The dynamical model takes into account the diffusion of cells, the de-differentiation (or plasticity) mechanism of differentiated cancer cells (DCs) and the time delay on the interaction between microRNAs molecules (microRNAs) with DCs. The stability of the model system is studied by using a Hopf bifurcation analysis. We mainly investigate on the critical time delay τc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _{c}$$\\end{document}, that represents the time for DCs to transform into CSCs after the interaction of microRNAs with DCs. Using the system parameters, we calculate the value of τc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _{c}$$\\end{document} for prostate, lung and breast cancers. To confirm the analytical predictions, the numerical simulations are performed and show the formation of spatiotemporal circular patterns. Such patterns have been found as promising diagnostic and therapeutic value in management of cancer and various diseases. The radiotherapy is applied in the particular case of prostate model. We calculate the optimum dose of radiation and determine the probability of avoiding local cancer recurrence after radiotherapy treatment. We find numerically a complete eradication of patterns when the radiotherapy is applied before a time t<τc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t < \ au _{c}$$\\end{document}. This scenario induces microRNAs to act as suppressors as experimentally observed in prostate cancer. The results obtained in this paper will provide a better concept for the clinicians and oncologists to understand the complex dynamics of CSCs and to design more efficacious therapeutic strategies to prevent the non-recurrence of cancers.

Design and analysis of active disturbance rejection control for time-delay systems using frequency-sweeping

For the typical first-order systems with time-delay, this paper explors the control capability of linear active disturbance rejection control (LADRC). Firstly, the critical time-delay of LADRC is analyzed using the frequency-sweeping method and the Routh criterion, and the stable time-delay interval starting from zero is accurately obtained, which reveals the limitations of general LADRC on large time-delay. Then in view of the large time-delay, an LADRC controller is developed and verified to be effective, along with the robustness analysis. Finally, numerical simulations show the accuracy of critical time-delay, and demonstrate the effectiveness and robustness of the proposed controller compared with other modified LADRCs.

Seeking Velocity-Free Consensus for Multi-Agent Systems With Nonuniform Communication and Measurement Delays

This paper addresses the consensus control problem of nonuniform delayed multi-agent systems without velocity measurements, and further obtains an explicit expression for the delay margin condition (critical time delay). Firstly, the passivity-based control technique is introduced to design the nominal consensus controller, which can enhance the robustness of the system by injecting additional relative damping. Then, the system states and the virtual state of the damping term are incrementally generalized into a third-order equation. Based on the frequency domain method, this equation was transformed into a high-order polynomial. Thus, the consensus conditions of the delayed multi-agent system are obtained according to the monotonicity of the polynomial. In detail, the conditions are presented in the form of an upper bound on the time delays and inequality sets of controller parameters. Finally, the effectiveness of the proposed controller and its corresponding consensus conditions are verified by designing the numerical simulation experiments.

Evolutionary game dynamics of cooperation in prisoner's dilemma with time delay.

Cooperation is an indispensable behavior in biological systems. In the prisoner's dilemma, due to the individual's selfish psychology, the defector is in the dominant position finally, which results in a social dilemma. In this paper, we discuss the replicator dynamics of the prisoner's dilemma with penalty and mutation. We first discuss the equilibria and stability of the prisoner's dilemma with a penalty. Then, the critical delay of the bifurcation with the payoff delay as the bifurcation parameter is obtained. In addition, considering the case of player mutation based on penalty, we analyze the two-delay system containing payoff delay and mutation delay and find the critical delay of Hopf bifurcation. Theoretical analysis and numerical simulations show that cooperative and defective strategies coexist when only a penalty is added. The larger the penalty is, the more players tend to cooperate, and the critical time delay of the time-delay system decreases with the increase in penalty. The addition of mutation has little effect on the strategy chosen by players. The two-time delay also causes oscillation.

Correlation and causality between carbon and energy markets: a complexity perspective.

Global warming obliges humans to focus on the relationships between carbon and energy markets. This study considers the relationship between carbon and energy markets from a complexity perspective. Chinese carbon prices and four energy indexes are selected as empirical variables. First, the complexities of carbon and energy markets are measured by multi-scale fuzzy entropy. The critical time delay of the series is then obtained by maximizing the Pearson coefficients between these markets. Further, analysis of the detrended cross-correlation coefficient confirms the existence of time delay. Finally, transfer entropy is applied to investigate the causality pertaining to dynamic complexity. Results of fuzzy entropy analysis reveal that the carbon market has lower complexity than energy markets. Meanwhile, multi-scale results indicate greater complexity on the small time scales in all markets than on the large time scales. The critical time delay is found to be about 50, which maximizes the correlation coefficient. Finally, causality between carbon and energy markets varies. Expectations in the carbon market impact oil gas and coal markets; electricity and new energy affect the carbon market; and cross-causality exists in the relationship between coal and carbon markets. The participants should focus on the information transmission between carbon and energy markets.

Toward a big picture of COVID-19.

The paper aims to illustrate and explain the problems and opportunities for improvement in Covid management that become evident when taking a systems perspective. Critical time delays occurred in the regulation of the pandemic that the management cycle of political cybernetics makes explicit. In general, the executive management of the pandemic in global, regional, and national organizations was unprepared in detecting and responding to the onset of the waves and making appropriate decisions towards differential instead of general lockdowns based on available data. This was further complicated by the mutants of SARS‐CoV2 that perpetuated the high dynamics of the pandemic. In addition, the diversity of medical specialisms, without appropriate big picture thinking, led to an imbalanced response that failed to appreciate the role of virology and epidemiology compared to clinical and public health‐related issues. In consequence, laboratory experts suggested everyday regulations for the citizens without taking into account wider considerations for empirical research. There was an insufficient effort made for proposed treatment studies using existing agents based on the established understanding of essential physiology and the role of local and systemic chronic inflammation. In contrast, driven by media popularization, drugs that later proved beneficial were put in doubt and other drugs that lacked benefit and potentially caused harm were driven to clinical trials and utilization. Person‐centered systems view backed by scientific knowledge and established data would have set better priorities. Finally, we need to take a step back and consider the Corona crisis pandemic in the context of the unidimensional utility‐driven handling of natural ecosystems by the culture of industrialized countries. This ever‐accelerating destruction of life spaces for species drives adaptations are the basis of zoonoses. There is strong evidence that future pandemics should be faced with a more systemic socio‐ecological conceptual framework that also reflects the fatal impact of human civilization on natural ecosystems, no matter if SARS CoV2 is a zoonosis or a laboratory accident. It is critical for the future of our species that we collectively learn from this experience, address limitations in our perspectives, enhance our system‐based science and bolster global, regional, and national crisis management. The impact of climate change and biodiversity loss has crossed the horizon and is now clearly in full sight.

Mutual Synchronization of Spatially Distributed 24 GHz Oscillators up to Distances of 500 m

This brief studies how mutual synchronization of oscillators can be achieved for cross-coupling time delays much larger than the period of the oscillations. Using the closed loop transfer function for a system of two mutually delay-coupled phase-locked loops (PLLs) and applying the Nyquist stability criterion, the critical time delay for which stable in- and anti-phase synchronized states become unstable is calculated. The analysis reveals the range of feed-forward loop gains for a given time delay value so that stable in- or anti-phase synchronized states can exist. These theoretical predictions are then verified by measurements with PLLs operating at 24GHz and for cross-coupling time delays ranging from the nano- to the microseconds domain. Such delays are equivalent to coupling at distances of up to 500m. The experimental results show a good agreement with the theoretical predictions. Hence, this brief shows how to setup a network of mutually delay-coupled PLLs and achieve stable synchronized states for a given time delay.

An LBL positioning algorithm based on an EMD\u2013ML hybrid method

Autonomous underwater vehicles (AUVs) are essential assets for ocean exploration requiring reliable underwater positioning technology. Aiming to improve the latter technology in a low SNR and reverberation environment, the Chan–Taylor hybrid positioning algorithm establishes a long-baseline system (LBL) based on the time difference of arrival (TDOA) by reducing the number of sensors required while preserving the positioning accuracy. However, the traditional LBL algorithm’s accuracy is reduced due to the critical time delay estimation under such environmental conditions. Hence, this paper suggests a new LBL positioning technology relying on an empirical mode decomposition (EMD) to construct a filter function combined with the maximum likelihood (ML) estimation method. MATLAB/Simulink is applied to establish the simulation environment of LBL localization system, simulating the AUV motion under 5–30 dB SNR. This paper analyzes the accuracy of TDOA by generalizing the cross-correlation method (GCC), phase transform (PHAT), ML, and EMD–ML. Based on the TDOA value obtained by the EMD–ML filtering algorithm, the positioning errors of the Chan–Taylor hybrid positioning algorithm and the Chan algorithm are compared. The results show that comparative synthetic evaluations against the traditional GCC demonstrate that the proposed method has a higher time delay estimation accuracy within a reverberation environment with SNR less than 15 dB. The Chan–Taylor hybrid positioning algorithm limits the errors of the CHAN algorithm and improves the overall positioning system accuracy.

Replicator dynamics of division of labor games with delayed payoffs in infinite populations

In recent years, the division of labor game has received widespread attention, however, the time delay in payoffs has been ignored. Hence, in this paper, we consider that there is a time delay for the player to gain the payoffs in the game, and the delay in payoffs leads to a Hopf bifurcation. When the time delay is greater than the critical time delay, the replicator dynamics oscillates near the equilibrium point, the critical time delay is determined by the cost difference between the two tasks and the cooperation benefits between the two players. We obtain the expression of the critical time delay by applying the characteristic equation analysis method, and clearly analyze various cases through observation and numerical simulation. With the increase of time delays, the dynamic system shows a transition from asymptotic stability to oscillation near equilibrium.

Delay-Dependent Sliding Mode Variable Structure Control of Vehicle Magneto-Rheological Semi-Active Suspension

The vehicle semi-active suspension with Magneto-Rheological Damper (MRD) has been a hot research topic of this decade, featuring the challenging task of the robust control with actuator time delay considerations. In this study, a delay dependent sliding mode variable structure control, based on the Linear Matrix Inequality (LMI), is proposed to suppress the vibration of the Magneto-Rheological Semi-Active Suspension (MRSS) control system. In accordance with the nonlinear characteristics of MRD, a dynamic model of automotive semi-active suspension system, considering time delay, is established. By defining a parameter-dependent Lyapunov switching functional, the conditions for asymptotic stability of closed-loop time delay system are derived, while the sliding mode variable structure control with reduced conservatism is designed. According to the method of LMI, the asymptotic stability problem of sliding mode is transformed into a feasibility problem, which can be solved by the solver ‘feasp’ in LMI toolbox. In addition, the calculation of the critical time delay of MRSS is expressed as a generalized eigenvalue optimization problem. For comparison purposes, three representative controllers, including a conventional sliding mode controller, a delay dependent controller, and a smith compensation, are studied. Simulation and real vehicle testing on bump and random road responses show that, the designed delay dependent controller can ensure the stability of the suspension system, weaken the influence of time delay on the control performance and effectively improve the ride comfort of the vehicle.

Analysis of an Active/Passive Postural Quiet Stance Regulation Model: Perfect Behavior and Critical Characteristics

In this work, we investigate the human quiet stance regulation problem using a single-link inverted pendulum model in the sagittal plane via the ankle joint's passive/active torques’ actions. The active torque consists of ankle muscle contractions that are activated by the delayed action of the Central Nervous System (neural controller). The passive torque is related to the intrinsic mechanical properties of the muscle-tendon-ligament component. The failure of the human quiet stance is then directly related to the failure of one or both types of torques. We propose to model the neural controller as a delayed Proportional-Derivative-Acceleration controller acting on the ankle joint's angular position. By using the multiplicity-induced-dominancy property, the critical time delay of the motor control and the critical ankle-joint stiffness are both investigated.

Stability analysis of the anti-lock braking system with time delay

A time delay exists between driver input and vehicle braking state response during the working process of the anti-lock braking system (ABS), and the braking performance of vehicles will be further reduced due to the delay of controllers. This paper investigates a systematic method of stability analysis for time delay ABS, and the analysis focuses on the stability and critical delay algorithm of ABS with delay time. Firstly, the dynamic structure and modelling process of ABS are briefly introduced, and PD control algorithm is adopted to improve the control performance. Then, dynamic models of ABS with time delay are derived, and the full delay stability interval and critical time delay algorithm of ABS are deduced by using the generalized Sturm criterion method. Finally, the validity of the critical delay algorithm by the proposed method and the stability and accuracy of ABS with time delay, different road conditions, vehicle speeds and control parameters are illustrated by numerical simulations, and the results show that the critical time delay algorithm of ABS can be verified under different conditions.

Flutter instability and active aeroelastic control with time delay for a two-dimensional airfoil

This paper studies the stability of a two-dimensional controlled airfoil system with time delay. First of all, a hybrid approach based on the frequency sweep test and the eigenvalue problem approximation using the Taylor series expansion of the delayed term is proposed to predict the critical time delay as well as the angular frequency of flutter instability. The efficiency of the proposed approach is illustrated by numerical examples for the prediction of self-sustaining vibrations of a phenomenological airfoil model with two degrees of freedom. One point of interest is to bring an understanding of the physical phenomena of the dynamic behavior involved in the appearance of flutter for the controlled airfoil system with time delay. Numerical results indicate that although one active controller is effective in suppressing airfoil flutter in a controlled system without time delay, control failure may happen depending on the time delay in control design. Secondly not only the effectiveness but also some drawbacks of two proposed controllers, namely the linear quadratic regulator state-feedback controller and the pole placement approach, are discussed through numerical simulations.

Theoretical and experimental studies on critical time delay of multi-DOF real-time hybrid simulation

Theoretical and experimental studies on critical time delay of multi-DOF real-time hybrid simulation

HOPF bifurcation and stability conditions for a class of nonlinear mass regulation systems with delay

The underwater glider platform is equipped with a mass block adjustment system, which can directly control the roll angle and pitch angle through mass block adjustment, and indirectly control the heading angle through the coupling of profile motion. As the underwater glider energy and space limitations drive the low power and low frequency control, it will inevitably lead to the underwater glider attitude adjustment process is subject to the delay problem of mass motion state signal feedback, the delay time and the nonlinear and coupling characteristics fused together more likely to cause the instability of the control system. In this paper, the time delay problem in the attitude control of underwater glider is summarized as a class of nonlinear stability problems with time delay parameters. The HOPF bifurcation phenomenon caused by the time delay parameter is discussed, and the critical time delay conditions for HOPF bifurcation generation are given. The effect of the time delay parameter on the bifurcation direction and the stability of the periodic solution is analyzed using the central flow pattern method. Finally, the correctness of the theoretical analysis is verified by numerical simulation, which provides a theoretical basis for the platform stability control and drive system design of the underwater glider.

Global $5.1 bn photocatalysts technologies and markets, 2020-2021 & 2021-2026

The underwater glider platform is equipped with a mass block adjustment system, which can directly control the roll angle and pitch angle through mass block adjustment, and indirectly control the heading angle through the coupling of profile motion. As the underwater glider energy and space limitations drive the low power and low frequency control, it will inevitably lead to the underwater glider attitude adjustment process is subject to the delay problem of mass motion state signal feedback, the delay time and the nonlinear and coupling characteristics fused together more likely to cause the instability of the control system. In this paper, the time delay problem in the attitude control of underwater glider is summarized as a class of nonlinear stability problems with time delay parameters. The HOPF bifurcation phenomenon caused by the time delay parameter is discussed, and the critical time delay conditions for HOPF bifurcation generation are given. The effect of the time delay parameter on the bifurcation direction and the stability of the periodic solution is analyzed using the central flow pattern method. Finally, the correctness of the theoretical analysis is verified by numerical simulation, which provides a theoretical basis for the platform stability control and drive system design of the underwater glider.

Hopf bifurcation of a delayed reaction–diffusion model with advection term

This article focus on the Hopf bifurcation of a delayed reaction–diffusion equation with advection term subject to Dirichlet boundary and no-flux boundary conditions in a bounded domain, respectively. It is shown that the existence of spatially non-homogeneous steady-state solutions will be obtained when the parameter λ of the model (9) closes to the principle eigenvalue λ1 of the elliptic operator Lλ. Moreover, a supercritical Hopf bifurcation occurs near the non-homogeneous positive steady-state at a series critical time delay values. Finally, we elucidate the effect of advection on Hopf bifurcation values. It is worth noting that the advective effect has accelerated the generation of Hopf bifurcation to a certain extent.

Replicator dynamics of an N-player snowdrift game with delayed payoffs

We consider a version of the N-player snowdrift game in which the payoffs obtained by the players are delayed. The delay in payoffs is shown to lead to a Hopf bifurcation with an associated critical value of the time delay in the replicator dynamics. For time delays larger than the critical time delay, the replicator dynamics oscillate around the equilibrium instead of asymptotically approaching it. The dependence of this critical time delay on the parameters of the game is determined. After developing the analysis for the 2-player game, the same methodology is applied to the N-player version of the game to show how the results change as a function of N, concluding with an analysis of the limiting case of large numbers of players.

Active vibration control and stability analysis of a time-delay system subjected to friction-induced vibration

The use of active vibration control may induce a delay leading to detrimental degradation of the performance of active vibration control. This is particularly true in the case of mechanical systems subjected to friction-induced vibration and noise for which such time-delays can lead to the appearance of undesirable instability. Furthermore, conducting a stability analysis of time-delay systems and estimation of the critical time delay are challenging, due to the infinite nature of the characteristic (quasi) polynomial of the associated closed-loop system, having an infinite number of roots.The objective of this paper is to discuss a strategy for the estimation of the critical time delay for the problem of Friction-Induced Vibration and noisE (FIVE). To achieve such an objective, the prediction of the stability analysis of time delay systems and the estimation of the associated critical time delay are first performed by applying the frequency sweep test and the eigenvalue problem approximation using the Taylor series expansion of the delayed term. In a second time, a mixed approach is proposed to predict effectively the real critical time delay of autonomous controlled systems subjected to friction-induced vibration. The efficiency of the proposed approach is illustrated by numerical examples for the prediction of self-sustaining vibrations of a phenomenological model with two degrees of freedom for which it is possible to provide a clear understanding and illustration of the phenomena involved and observed.