We introduce a new non-abelian quantum synchronisation model over the unitary group, represented as a gradient flow, where state matrices asymptotically converge to a common one up to phase translation. We provide a sufficient framework leading to quantum synchronisation based on Riccati-type differential inequalities. In addition, uniform time-delayed interaction is considered for modelling realistic communication, and we demonstrate that quantum synchronisation is persistent when a small time delay is allowed. Finally, numerical simulation is performed to visualise qualitative behaviours and support theoretical results.

This paper is concerned with stochastic Schrödinger delay lattice systems with both locally Lipschitz drift and diffusion terms. Based on the uniform estimates and the equicontinuity of the segment of the solution in probability, we show the tightness of a family of probability distributions of the solution and its segment process, and hence the existence of invariant measures on $l^2\times L^2((-\rho,\,0);l^2)$ with $\rho >0$. We also establish a large deviation principle for the solutions with small noise by the weak convergence method.

Age dynamics of the ability of cercariae of two digenean species, Himasthla elongata (Himasthlidae) and Renicola parvicaudatus (Renicolidae), to infect the second intermediate host (SIH), mussels (Mytilus edulis), was investigated experimentally. This is the first study of this kind made on cercariae transmitted in the intertidal of the northern seas. The larvae of all tested ages (from 0.5 to 6 hr) were equally successful in infecting mussels. This finding disagrees with the literature data on cercariae of several freshwater digeneans, which are practically incapable of infecting the SIH during the first 1–3 hr of life. The presence of a time delay before the attainment of the maximum infectivity (TDMI) may be associated with the need for physiological maturation of cercariae in the very beginning of their life in the environment, the need for their broad dispersion, and the prevention of superinfection of the downstream host. The absence of TDMI in the cercariae examined in our study could be associated with the instability of environmental factors in the marine intertidal (wave impact, tidal currents). These factors promote a broad dispersion of cercariae in the intertidal biotope and prevent superinfection of potential SIHs. Biological and behavioural features may also play a role. We hypothesize that the presence or absence of TDMI does not depend on the taxonomic affiliation of the cercariae but is determined by the transmission conditions.

We show that, contrary to simple predictions, most AGNs show at best only a small increase of lags with increasing wavelength in the J, H, K, and L bands. We suggest that a possible cause of this near simultaneity from the near-IR to the mid-IR is that the hot dust is in a hollow bi-conical outflow of which we preferentially see the near side. In the proposed model sublimation or re-creation of dust (with some delay relative luminosity variations) along our line of sight in the hollow cone as the flux varies could be a factor in explaining the AGN changing-look phenomenon (CL). Variations in the dust obscuration can help explain changes in relationship of Hβ time delay on Luv variability. The relative wavelength independence of IR lags simplifies the use of IR lags for estimating cosmological parameters.

This paper is concerned with a nonlocal reaction–diffusion system with double free boundaries and two time delays. The free boundary problem describes the evolution of faecally–orally transmitted diseases. We first show the well-posedness of global solution, and then establish the monotonicity and asymptotic property of basic reproduction number for the epidemic model without delays, which is defined by spectral radius of the next infection operator. By introducing the generalized principal eigenvalue defined in general domain, we obtain an upper bound of the limit value of basic reproduction number. We discuss the spreading and vanishing phenomena in terms of the basic production number. By employing the perturbed approximation method and monotone iteration method, we establish the existence, uniqueness and monotonicity of solution to semi-wave problem. When spreading occurs, we determine the asymptotic spreading speeds of free boundaries by constructing suitable upper and lower solutions from the semi-wave solutions. Moreover, spreading speeds for partially degenerate diffusion case are provided in a similar way.

A delayed reaction-diffusion system with free boundaries is investigated in this paper to understand how the bacteria spread spatially to larger area from the initial infected habitat. Under the assumptions that the nonlinearities are of monostable type and the initial values satisfy some compatible condition, we show that the free boundary problem is well-posed and discuss the long-time behaviour of solution (including spreading and vanishing) in terms of the spatial-temporal risk index. Furthermore, to determine the spreading speed of free boundaries when spreading occurs, we first study the distribution of roots of a transcendental equation containing a polynomial of degree four and then establish the existence and uniqueness of monotone solution to a delay-induced nonlocal semi-wave problem by employing the approximation method, lower-upper solutions technique and Schauder fixed point theorem. It is shown that time delays slow down the spreading of bacteria.

Ethnographers have recorded many instances of tokens donated as gifts to attract new partners or strengthen ties to existing ones. We study whether gifts are an effective pledge of the donor’s trustworthiness through an experiment modeled on the trust game. We vary whether the trustee can send a token before the trustor decides whether to transfer money; whether one of the tokens is rendered salient through experimental manipulations (a vote or an incentive-compatible rule of purchase for the tokens); and whether the subjects interact repeatedly or are randomly re-matched in each round. Tokens are frequently sent in all studies in which tokens are available, but repeated interaction, rather than gifts, is the leading behavioral driver in our data. In the studies with random pairs, trustors send significantly more points when the trustee has sent a token. Subjects in a fixed matching achieve comparable levels of trust and trustworthiness in the studies with and without tokens. The trustee’s decision to send a token is not predictive of the amount the trustee returns to the trustor. A token is used more sparingly whenever salient — a novel instance of endogenous value creation in the lab.

Manipulations for activating reflective thinking, although regularly used in the literature, have not previously been systematically compared. There are growing concerns about the effectiveness of these methods as well as increasing demand for them. Here, we study five promising reflection manipulations using an objective performance measure — the Cognitive Reflection Test 2 (CRT-2). In our large-scale preregistered online experiment (N = 1,748), we compared a passive and an active control condition with time delay, memory recall, decision justification, debiasing training, and combination of debiasing training and decision justification. We found no evidence that online versions of the two regularly used reflection conditions — time delay and memory recall — improve cognitive performance. Instead, our study isolated two less familiar methods that can effectively and rapidly activate reflective thinking: (1) a brief debiasing training, designed to avoid common cognitive biases and increase reflection, and (2) simply asking participants to justify their decisions.

In view of the cooperative guidance problem with time delay, this paper proposes a two-stage time-delay prescribed-time cooperative guidance law in the three-dimensional (3D) space. In the first stage, by introducing a time scaling function and time-delay consensus, the proposed cooperative guidance law can overcome the negative influence of time delay to guaranteed the desired convergence performance. Derived from the Lyapunov convergence analysis, the time-delay stability of the first stage can be ensured and the convergence time can be described as the relationship between delayed time and mission-assigned convergence time. Then, taking the prescribed-time-related convergence time as the switching point, the second stage begins with suitable initial conditions and all interceptors are governed by proportional navigation guidance. Finally, comparative simulations are performed to demonstrate the effectiveness and superiority of the proposed time-delay guidance law.

Based on the fact that the incubation periods of epidemic disease in asymptomatically infected and infected individuals are inevitable and different, we propose a diffusive susceptible, asymptomatically infected, symptomatically infected and vaccinated (SAIV) epidemic model with delays in this paper. To see whether epidemic disease can propagate spatially with a constant speed, we focus on the travelling wave solution for this model. When the basic reproduction number of the corresponding spatial-homogenous delayed differential system is greater than one and the wave speed is greater than or equal to the critical speed, we prove that this model admits nontrivial positive travelling wave solutions. Our theoretical results are of benefit to the prevention and control of epidemic.

In this paper, the k-valued logic control network is introduced to study the cooperative pursuit control problem of multiple underactuated underwater vehicles (UUVs) with time delay in three-dimensional space. The semi-tensor product of matrices is used to solve the complex calculation problem of the large dimension matrix. The influence of communication delay on multiple UUVs’ optimization and cooperative pursuit control is expressed in a matrix. Under the leadership of evader UUV, the control algorithm can ensure that all the pursuit UUVs reach the desired position. The stability of the closed loop system is proved.

Stability is a major problem with bilateral teleoperator when there is a transmission time delay. By adding adequate damping gain into position servo, a stable bilateral control can be achieved under the existence of time delay. However, large damping gain is required to stabilize the system and the performance is degraded. In this paper, the performance improvement by introducing a high-pass filter into a proportional derivative-based teleoperator with time delay has been studied. We proposed new control law and derived the stability condition. We demonstrated the performance improvement using a hybrid matrix, 1-degree of freedom (DOF), 2-DOF simulations, and 2-DOF peg-in-hole experiments.

This document proposes a control scheme for delayed bilateral teleoperation of a mobile robot, which it is sought to achieve a coordination of the master device position with the slave mobile robot velocity, and at the same time synchronize the force exerted by the operator with force applied by the environment over the mobile robot. This approach allows the operator to improve the sensitive perception of the remote environment in which the robot navigates while he generates commands to control the mobile robot motion. In this paper, variable and asymmetrical communication time delays are taken into account, as well as a non-passive model of the human operator, for which a novel model is proposed that has a more general structure than the typical ones used to date in the teleoperation field. Furthermore, based on the theoretical analysis presented, the state of convergence in the stationary response is obtained. In addition, an experimental performance evaluation is carried out, where the position–velocity error, force error and the time to complete the task are evaluated. In the tests, a human operator commands a remote mobile robot to push objects of different weight while he perceives the weight of each object through the force feedback system. As an outcome, the theoretical and practical results obtained allow concluding that a satisfactory trade-off between stability and transparency is reached.

Multiple trait selection indexes in pig breeding programmes should take into account the population structure and time delay between parent selection and expressions of traits in all production levels next to the trait impacts on economic efficiency of production systems. Gene flow procedures could be used for the correct evaluation of maternal and direct traits of pig breeds involved in breeding or crossbreeding systems. Therefore, the aim of this study was to expand a previously developed bioeconomic model and computer program to calculate the marginal economic values by including a gene flow procedure to calculate the economic weights for maternal and direct traits in pig breeds. The new program was then applied to the three-way crossbreeding system of the Czech National Programme for Pig Breeding. Using this program, the marginal economic values of traits for dam breeds Czech Large White in the dam position and Czech Landrace in the sire position, and for the sire breed Pietrain were weighted by the number of discounted gene expressions of selected parents of each breed summarised within all links of the crossbreeding system during the 8-year investment period. Economic weights calculated in this way were compared with the approximate economic weights calculated previously without a gene flow procedure. Taking into account the time delay between parent selection and trait expression (using discounting with half-year discount rates of 2% or 5%) and including more than one generation of parent progeny had little impact on the relative economic importance of maternal and direct traits of breeds involved in the evaluated three-way crossbreeding system. These results indicated that this gene-flow method could be foregone when estimating the relative economic weights of traits in pig crossbreeding systems applying artificial insemination at all production levels.

We study a delayed fuzzy $H_{\infty }$ control problem for an offshore platform under external wave forces. First, by considering perturbations of the masses of the platform and an active mass damper, a Takagi–Sugeno fuzzy model is established. Then, by introducing time delays into the control channel, a delayed fuzzy state feedback $H_{\infty }$ controller is designed. Simulation results show that the delayed fuzzy state feedback $H_{\infty }$ controller can reduce vibration amplitudes of the offshore platform and can save control cost significantly.

We investigate delayed state feedback control of a periodic-review inventory management system with perishable goods. The stock under consideration is replenished from multiple supply sources. By using delayed states as well as current states of the inventory system, a delayed feedback $H_{\infty }$ control strategy is developed to mitigate bullwhip effects of the system. Some conditions on the existence of the delayed feedback $H_{\infty }$ controller are derived. It is found through simulation results that the proposed delayed $H_{\infty }$ control scheme is capable of improving the performance of the inventory management significantly. In addition, the delayed controller is better than the traditional delay-free $H_{\infty }$ controller.

A modified predator-prey system described by two differential equations and an algebraic equation is discussed. Formulae for determining the direction of a Hopf bifurcation and the stability of the bifurcating periodic solutions are derived differential-algebraic system theory, bifurcation theory and centre manifold theory. Numerical simulations illustrate the results, which includes quite complex dynamical behaviour.

This paper analyzes the existence of Hopf bifurcation and establishes the conditions under which the equilibrium path converges toward periodic solutions in a one-sector optimal growth model with delay. We establish the limits and the possibilities of nonlinear dynamics (i.e., cycles) vis-à-vis delays. In particular, we formulate a new method to further comprehend the root distribution of the characteristic equation of a standard optimal growth model with delayed investment structure. We show that nonmonotonic dynamics (limit cycles, persistent oscillations) occurs when the delayed investment causes permanent adjustment failures among the economic variables in the economy.

In this paper, a nonlinear stage-structured model for Lyme disease is considered. The model is a system of diòerential equations with two time delays. We derive the basic reproductive rate ${{R}_{0}}\left( {{\tau }_{1}},\,{{\tau }_{2}} \right)$. If ${{R}_{0}}\left( {{\tau }_{1}},\,{{\tau }_{2}} \right)\,<\,1$, then the boundary equilibrium is globally asymptotically stable. If ${{R}_{0}}\left( {{\tau }_{1}},\,{{\tau }_{2}} \right)\,>\,1$, then there exists a unique positive equilibrium whose local asymptotic stability and the existence of Hopf bifurcations are established by analyzing the distribution of the characteristic values. An explicit algorithm for determining the direction of Hopf bifurcations and the stability of the bifurcating periodic solutions is derived by using the normal form and the center manifold theory. Some numerical simulations are performed to confirm the correctness of theoretical analysis. Finally, some conclusions are given.

This paper proposes a globally and exponentially convergent predictive observer for attitude and position estimation based on landmark measurements and velocity (angular and linear) readings. It is assumed that landmark measurements are available with time-delay. The maximum value of the sensor delay under which the estimation error converges to zero is calculated. Synthesis of the observer is based on a representation of rigid-body kinematics and sensor delay, formulated via ordinary and partial differential equations (ODE-PDE). Observability condition specifies necessary and sufficient landmark configuration for convergence of attitude and position estimation error to zero. Finally, for implementation purposes, a PDE-free realization of the predictive observer is proposed. Simulation results are presented to demonstrate performance and convergence properties of the predictive observer in case of a wheeled mobile robot.