Oscillation of Half-Linear Differential Equations with Delay by Simona Fišnarová, Robert Mařík

“…We study the half-linear delay differential equation , , We establish a new a priori bound for the nonoscillatory solution of this equation and utilize this bound to derive new oscillation criteria for this equation in terms of oscillation criteria for an ordinary half-linear differential equation. …”
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Disease dynamics for the hometown of migrant workers by Ram P. Sigdel, C. Connell McCluskey

“…Biol. 300:100--109 (2012) formulatedand studied a delay differential equation model for disease dynamics in a region where a portionof the population leaves to work in a different region for an extended fixed period. …”
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Dynamics of a Stage Structured Pest Control Model in a Polluted Environment with Pulse Pollution Input by Bing Liu, Ling Xu, Baolin Kang

“…By using pollution model and impulsive delay differential equation, we formulate a pest control model with stage structure for natural enemy in a polluted environment by introducing a constant periodic pollutant input and killing pest at different fixed moments and investigate the dynamics of such a system. …”
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Note on oscillation of neutral differential equations with multiple delays by Petr Hasil, Michal Pospíšil, Lucia Pospíšilová Škripková, Michal Veselý

“…This note is a reaction on a recently published sufficient condition for oscillation of all solutions of a neutral delay differential equation. It is shown by a counterexample that the result is not correct and the problem is explained in details. …”
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Effect of time delay on a detritus-based ecosystem by Nurul Huda Gazi, Malay Bandyopadhyay

“…Next, we have introduced discrete time delay due to recycling of dead organic matters and gestation of nutrients to the growth equations of various trophic levels. With delay differential equation model system we have studied the effect of time delay on the stability behaviour. …”
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Hopf Bifurcation in a Cobweb Model with Discrete Time Delays by Luca Gori, Luca Guerrini, Mauro Sodini

“…The dynamics of the economy is characterised by a one-dimensional delay differential equation. In this context, we show that (1) if the elasticity of market demand is sufficiently high, the steady-state equilibrium is locally asymptotically stable and (2) if the elasticity of market demand is sufficiently low, quasiperiodic oscillations emerge when the time lag (that represents the length of production cycle) is high enough.…”
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Multiple Nonlinear Oscillations in a 𝔻3×𝔻3-Symmetrical Coupled System of Identical Cells with Delays by Haijun Hu, Li Liu, Jie Mao

“…The individual cells are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. …”
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Global attractivity of positive periodic solutions for an impulsive delay periodic food limited population model by Jian Song

“…We will consider the following nonlinear impulsive delay differential equation N′(t)=r(t)N(t)((K(t)−N(t−mw))/(K(t)+λ(t)N(t−mw))), a.e. t>0, t≠tk, N(tk+)=(1+bk)N(tk), K=1,2,…, where m is a positive integer, r(t), K(t), λ(t) are positive periodic functions of periodic ω. …”
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Oscillation of Second-Order Nonlinear Delay Dynamic Equations with Damping on Time Scales by H. A. Agwa, Ahmed M. M. Khodier, Heba A. Hassan

“…Also, our results unify the oscillation of the second-order nonlinear delay differential equation with damping and the second-order nonlinear delay difference equation with damping. …”
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Dynamics Analysis of a Class of Delayed Economic Model by Chuangxia Huang, Changlin Peng, Xiaohong Chen, Fenghua Wen

“…This investigation aims at developing a methodology to establish stability and bifurcation dynamics generated by a class of delayed economic model, whose state variable is described by the scalar delay differential equation of the form d2p(t)/dt2=−μδ(p(t))(dp(t)/dt)−μbp(t−τ1) −μ(a0p(t−τ2)/(a1+p(t−τ2)))+μ(d0−g0). …”
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Dynamics of evolutionary competition between budding and lytic viral release strategies by Xiulan Lai, Xingfu Zou

“…In this paper, we consider the evolutionary competition between budding and lytic viral release strategies, using a delay differential equation model with distributed delay. When antibody is not established, the dynamics of competition depends on the respective basic reproductive ratios of the two viruses. …”
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Newton–Simpson-based predictor–corrector methods for milling chatter stability prediction by Yongjian Ji, Xiaokang Xu, Yulin Yang, Runnan Liu, Shuyao Liu, Zhenghu Yan

“…Firstly, the milling delay differential equation is transformed into the state space form, and then the time-delayed term and the periodic coefficient matrix of the state space equation are treated as an operator. …”
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On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays by Jaromír Baštinec, Leonid Berezansky, Josef Diblík, Zdeněk Šmarda

“…These conditions improve and extend some known oscillation results in the critical case for delay differential equations.…”
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Numerical Solution of Piecewise Constant Delay Systems Based on a Hybrid Framework by H. R. Marzban, S. Hajiabdolrahmani

“…An efficient numerical scheme for solving delay differential equations with a piecewise constant delay function is developed in this paper. …”
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SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects by Tongqian Zhang, Xinzhu Meng, Tonghua Zhang

“…We first propose a new epidemic disease model governed by system of impulsive delay differential equations. Then, based on theories for impulsive delay differential equations, we skillfully solve the difficulty in analyzing the global dynamical behavior of the model with pulse vaccination and impulsive population input effects at two different periodic moments. …”
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A New Comparison Principle for Impulsive Functional Differential Equations by Gang Li, Weizhong Ling, Changming Ding

“…Then, using this comparison principle, we obtain some sufficient conditions for several stabilities of impulsive delay differential equations. Finally, we present an example to show the effectiveness of our results.…”
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Culling structured hosts to eradicate vector-borne diseases by Xinli Hu, Yansheng Liu, Jianhong Wu

“…A compartmental model is developed, in the form of a nonautonomoussystem of delay differential equations subject to impulses atspecific times, for mosquito-born disease control involvinglarvicides and insecticide sprays. …”
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Sensitivity of dynamical systems to parameters in a convex subset of a topological vector space by H.T. Banks, S. Dediu, H.K. Nguyen

“…Schemes that approximate themeasures in the Prohorov sense are illustrated with numericalsimulations for distributed delay differential equations.…”
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Oscillation and Asymptotic Behavior of Higher-Order Nonlinear Differential Equations by J. Džurina, B. Baculíková

“…As a possible application of the lemma in the oscillation theory, we study the asymptotic properties and oscillation of the nth order delay differential equations (E)(r(t)[x(n−1)(t)]γ)′+q(t)xγ(τ(t))=0. …”
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Dynamic Properties of the Solow Model with Increasing or Decreasing Population and Time-to-Build Technology by Luca Guerrini, Mauro Sodini

“…The analytical results are obtained using the recent technique introduced by Beretta and Kuang (2002) in the studying of delayed differential equations with delay-dependent coefficients in characteristic equation. …”
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