Bifurcation Behavior and Hybrid Controller Design of a 2D Lotka–Volterra Commensal Symbiosis System Accompanying Delay by Qingyi Cui, Changjin Xu, Wei Ou, Yicheng Pang, Zixin Liu, Peiluan Li, Lingyun Yao

“…Making use of stability and bifurcation theory of delayed differential equation, we focus on the emergence of bifurcation behavior and stability nature of the formulated delayed Lotka–Volterra commensal symbiosis system. …”
Get full text

Effects of Climate Warming on Consumer-Resource Interactions: A Latitudinal Perspective by Priyanga Amarasekare

“…First, it uses delay differential equations to realistically depict the developmental delays inherent in ectotherm life cycles, and incorporates mechanistic descriptions of phenotypic trait responses, derived from first principles of thermodynamics, into the dynamical delay model. …”
Get full text

Reducing the Standstill Spacing and Duration of Safe Braking Control in Vehicle Platoons With Delays by Yun Meng, Zhuoyuan Wang

“…Therefore, delay differential equations are introduced to model the braking process, and a crossing criterion is introduced to establish the relationship between the control law and the braking process. …”
Get full text

Features of the Local Dynamics of the Opto-Electronic Oscillator Model with Delay by Elena V. Grigorieva, Sergey A. Kashchenko, Dmitry V. Glazkov

“…We consider electro-optic oscillator model which is described by a system of the delay differential equations (DDE). The essential feature of this model is a small parameter in front of a derivative that allows us to draw a conclusion about the action of processes with different order velocities. …”
Get full text

Complex Dynamics of a Predator–Prey Interaction with Fear Effect in Deterministic and Fluctuating Environments by Nirapada Santra, Sudeshna Mondal, Guruprasad Samanta

“…By analysing our system of nonlinear delay differential equations, we gain some insights into how fear and delays affect on population dynamics. …”
Get full text

Cascades of Periodic Solutions in a Neural Circuit With Delays and Slow-Fast Dynamics by Andrea Ferrario, James Rankin

“…We analyse periodic solutions in a system of four delayed differential equations forced by periodic inputs representing two competing neural populations connected with fast mutual excitation and slow delayed inhibition. …”
Get full text

Stability of Some Models in Mathematical Biology by Aldaikh, Abdalsalam B. H.

“…This concept should be taken into account, and this leads to the study of delay differential equations. However the mathematics required for the detailed analysis of the behaviour of such a model can be formidable, especially for biologists who share the subject. …”
Get full text

Wavelets operational methods for fractional differential equations and systems of fractional differential equations by Isah, Abdulnasir

“…A new operational matrix of fractional order derivative and integration based on this polynomial was also developed and used together with collocation method to solve FDEs, systems of FDEs and fractional order delay differential equations. Error bound for some of the considered problems is also shown and proved. …”
Get full text
Get full text

A time-delayed evolutionary game analysis of new energy vehicles development considering subsidy and carbon tax by Chunfeng Liu, Zixin Liu, Wenfang Li, Mengzhu Xu

“…Considering the possible delay effect of the game process, a time-delayed differential equation is established to analyze the effects of random time delay on the stability of the system. …”
Get full text

Application of the Fractional Calculus in Pharmacokinetic Compartmental Modeling by Tahmineh Azizi

“…Since tumor cells interactions are systems with memory, the fractional-order framework is a better approach to model the cancer phenomena rather than ordinary and delay differential equations. Therefore, the nonstandard finite difference analysis or NSFD method following the Grunwald-Letinkov discretization may be applied to discretize the model and obtain the fractional-order form to describe the fractal processes of drug movement in body. …”
Get full text

DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia by Christopher Rackauckas, Qing Nie

“…It covers discrete equations (function maps, discrete stochastic (Gillespie/Markov) simulations), ordinary differential equations, stochastic differential equations, algebraic differential equations, delay differential equations, hybrid differential equations, jump diffusions, and (stochastic) partial differential equations. …”
Get full text

صف من الطرائق الشرائحية بثلاث نقاط تجميعية لحل معادلات تفاضلية متأخرة by سليمان محمود

“… In this paper a study of the existence, uniqueness, stability and convergence of a class of C2-spline collocation methods for solving delay differential equations (DDEs) is introduced. The presented methods are based on C2-Spline with three collocation points , , and in each subinterval  It turns out that the proposed methods for DDEs are stable iff , and they possess convergence rate of order 6 if , in the remaining cases the order is 5. …”
Get full text

صف من الطرائق الشرائحية بثلاث نقاط تجميعية لحل معادلات تفاضلية متأخرة by سليمان محمود

“… In this paper a study of the existence, uniqueness, stability and convergence of a class of C2-spline collocation methods for solving delay differential equations (DDEs) is introduced. The presented methods are based on C2-Spline with three collocation points , , and in each subinterval  It turns out that the proposed methods for DDEs are stable iff , and they possess convergence rate of order 6 if , in the remaining cases the order is 5. …”
Get full text

Estimation of COVID-19 recovery and decease periods in Canada using delay model by Subhendu Paul, Emmanuel Lorin

“…Abstract We derive a novel model escorted by large scale compartments, based on a set of coupled delay differential equations with extensive delays, in order to estimate the incubation, recovery and decease periods of COVID-19, and more generally any infectious disease. …”
Get full text

Simulating brain resting-state activity: what matters? by Hadida, J

“…</p> <p>Mathematically, these models take the form of large systems of non-linear coupled delay-differential equations, and we implement software to numerically solve such systems efficiently. …”

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. …”

Synchronization and a secure communication scheme using optical star network by Theesar, S. Jeeva Sathya, Kamel Ariffin, Muhammad Rezal, Banerjee, Santo

“…The optical network is based on chaotic semiconductor laser (SL) systems described by dimensionless modified Lang-Kobayashi's (L-K) delay differential equations. The network nodes are mutually connected with a central semiconductor laser hub with bidirectional linear optical feedback. …”
Get full text

<i>PPF</i>-Dependent Fixed Point Results for Multi-Valued <i>ϕ</i>-<i>F</i>-Contractions in Banach Spaces and Applications by Mohammed M. M. Jaradat, Babak Mohammadi, Vahid Parvaneh, Hassen Aydi, Zead Mustafa

“…As applications of our PPF dependent fixed point results, we study the existence of solutions for delay differential equations (DDEs) which have numerous applications in population dynamics, bioscience problems and control engineering.…”
Get full text

Quantifying in vitro B. anthracis growth and PA production and decay: a mathematical modelling approach by Bevelynn Williams, Jamie Paterson, Helena J. Rawsthorne-Manning, Polly-Anne Jeffrey, Joseph J. Gillard, Grant Lythe, Thomas R. Laws, Martín López-García

“…We propose a single mathematical model, in terms of delay differential equations (DDEs), which can explain the in vitro dynamics of all three data sets. …”
Get full text

An Updated Method for Stability Analysis of Milling Process with Multiple and Distributed Time Delays and Its Application by Gang Jin, Wenshuo Li, Jianxin Han, Zhanjie Li, Gaofeng Hu, Guangxing Sun

“…After the dynamic of the combination milling process with variable helix cutter (VHC) and variable spindle speed (VSS) is modeled as linear delay differential equations with multiple and distributed time delays, the presented method is applied to carrying out its stability prediction for the first time. …”
Get full text