Bifurcation mechanism and hybrid control strategy of a finance model with delays by Zixin Liu, Wenfang Li, Changjin Xu, Chunfeng Liu, Dan Mu, Mengzhu Xu, Wei Ou, Qingyi Cui

“…Taking advantage of the stability criterion and bifurcation argument of delayed differential equation, we establish a delay-independent condition ensuring the stability and generation of Hopf bifurcation of the involved delayed finance model. …”
Get full text

Load Balancing for Mobility-on-Demand Systems by Durrant-Whyte, H., Roy, Nicholas, Abbeel, P.

“…The model takes the form of a set of nonlinear time-delay differential equations. We then show that the optimal rebalancing policy can be found as the solution to a linear program. …”
Get full text
Get full text

Stochastic modelling of time delay for solvent production by Clostridium Acetobutylicum P262 by Tawfiqullah, Ayoubi

“…Such phenomenon can be modelled via stochastic delay differential equations (SDDEs). Batch fermentation process is one of the systems which subject to the presence of uncontrolled fluctuation and delayed feedback. …”
Get full text

Investigation of the Processing Parameters Impact on the Flexural Tool Vibrations While Drilling by I. I. Ivanov, I. A. Kiselev, A. V. Koloskova

“…The system of delayed differential equations describing the reduced tool model dynamics was derived to estimate a dynamic stability of the drilling process. …”
Get full text

Dynamics and potential impact of the immune response to chronic myelogenous leukemia. by Peter S Kim, Peter P Lee, Doron Levy

“…We model the immune response using a system of delay differential equations, where the delay term accounts for the duration of cell division. …”
Get full text

Periodicity and dosage optimization of an RNAi model in eukaryotes cells by Tongle Ma, Yongzhen Pei, Changguo Li, Meixia Zhu

“…Firstly, by introducing both the degradation time delay τ 1 of mRNA caused by siRNA and the transportation time delay τ 2 of mRNA from the nucleus to the cytoplasm during protein translation, one acquires a novel delay differential equations (DDEs) model with physiology lags. …”
Get full text

On the Stability of Solutions of Neutral Differential Equations with Distributed Delay by T. K. Yskak

“…In addition, the method of modified Lyapunov–Krasovskii functionals allows to obtain estimates of solutions to linear systems of delay differential equations. Note that the use of modified Lyapunov–Krasovskii functionals also allows to obtain estimates of solutions to nonlinear differential equations and estimates of the attraction set. …”
Get full text

ON THE EQUIVALENCE OF DELAYED ARGUMENTS AND TRANSFER EQUATIONS FOR MODELING DYNAMIC SYSTEMS by V. A. Likhoshvai, T. M. Khlebodarova

“…In this paper, we considered a general form of a system of first-order delayed differential equations, traditionally used for describing the function of biological systems of different hierarchical levels. …”
Get full text

Generalized neural closure models with interpretability by Abhinav Gupta, Pierre F. J. Lermusiaux

“…In the present study, we simultaneously address all these challenges by developing the novel and versatile methodology of unified neural partial delay differential equations. We augment existing/low-fidelity dynamical models directly in their partial differential equation (PDE) forms with both Markovian and non-Markovian neural network (NN) closure parameterizations. …”
Get full text

Assessing the best time interval between doses in a two-dose vaccination regimen to reduce the number of deaths in an ongoing epidemic of SARS-CoV-2. by Leonardo Souto Ferreira, Otavio Canton, Rafael Lopes Paixão da Silva, Silas Poloni, Vítor Sudbrack, Marcelo Eduardo Borges, Caroline Franco, Flavia Maria Darcie Marquitti, José Cássio de Moraes, Maria Amélia de Sousa Mascena Veras, Roberto André Kraenkel, Renato Mendes Coutinho

“…Here we present a novel extended age-structured SEIR mathematical model that includes a two-dose vaccination schedule with a between-doses delay modelled through delay differential equations and linear optimization of vaccination rates. …”
Get full text

Neural closure models for dynamical systems by Gupta, Abhinav, Lermusiaux, Pierre

“…The new <jats:italic>neural closure models</jats:italic> augment low-fidelity models with neural delay differential equations (nDDEs), motivated by the Mori–Zwanzig formulation and the inherent delays in complex dynamical systems. …”
Get full text

Driven colloidal particles in optical potential energy landscapes by Bell-Davies, M

“…We observe a transition from diffusive to driven dynamics which is modelled using delay-differential equations. We find that this transition coincides with the maximum work done on the particle and a local minimum in the mutual information between the particle and the trap.…”

Application of the lumped age-class technique to studying the dynamics of malaria-mosquito-human interactions by Hancock, P, Godfray, H

“…The resulting model, phrased as a system of delay-differential equations, is only slightly harder to analyse than traditional ordinary differential equations and much easier than the alternative partial differential equation approach. …”

Tumour-natural killer and CD8+ T cells interaction model with delay by Awang, Nor Aziran, Maan, Normah, Sulain, Mohd. Dasuki

“…The interaction of the cells is described by a system of delay differential equations, and the delay, τ represent time taken for tumour cell reside interphase. …”
Get full text

Analysis of Dengue Transmission Dynamic Model by Stability and Hopf Bifurcation with Two-Time Delays by Prakash Raj Murugadoss, Venkatesh Ambalarajan, Vinoth Sivakumar, Prasantha Bharathi Dhandapani, Dumitru Baleanu

“…Results: Both endemic equilibrium and illness-free equilibrium were examined in terms of the stability theory of delay differential equations. As long as the basic reproduction number (R0) is less than unity, the illness-free equilibrium is locally asymptotically stable; however, when R0 exceeds unity, the equilibrium becomes unstable. …”
Get full text

A novel simulation-based analysis of a stochastic HIV model with the time delay using high order spectral collocation technique by Sami Ullah Khan, Saif Ullah, Shuo Li, Almetwally M. Mostafa, Muhammad Bilal Riaz, Nouf F. AlQahtani, Shewafera Wondimagegnhu Teklu

“…In this study, we present a novel mathematical model comprising a system of delay differential equations to describe the dynamics of intramural HIV infection. …”
Get full text

Global stability of a delayed SARS-CoV-2 reactivation model with logistic growth, antibody immunity and general incidence rate by A.M. Elaiw, A.J. Alsaedi, A.D. Hobiny

“…The model is formulated as a system of delay differential equations (DDEs). We establish that the model’s solutions are non-negative and ultimately bounded. …”
Get full text

Convergence Rate of the Diffused Split-Step Truncated Euler–Maruyama Method for Stochastic Pantograph Models with Lévy Leaps by Amr Abou-Senna, Ghada AlNemer, Yongchun Zhou, Boping Tian

“…This paper studies the stochastic pantograph model, which is considered a subcategory of stochastic delay differential equations. A more general jump process, which is called the Lévy process, is added to the model for better performance and modeling situations, having sudden changes and extreme events such as market crashes in finance. …”
Get full text

Downsizing of COVID-19 contact tracing in highly immune populations by Maria M. Martignoni, Josh Renault, Joseph Baafi, Amy Hurford

“…We present a delayed differential equation model to investigate how the immunity status and the relaxation of social distancing requirements affect contact tracing practices. …”
Get full text

Downsizing of COVID-19 contact tracing in highly immune populations. by Maria M Martignoni, Josh Renault, Joseph Baafi, Amy Hurford

“…We present a delayed differential equation model to investigate how the immunity status and the relaxation of social distancing requirements affect contact tracing practices. …”
Get full text