Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps by Guodong Liu, Xiaohong Wang, Xinzhu Meng, Shujing Gao

“…Furthermore, persistence in mean of the system is also investigated by using the theory of impulsive stochastic differential equations (ISDE) and delay differential equations (DDE). Finally, we carry out some simulations to verify our main results and explain the biological implications.…”
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Strong Convergence of a New Hybrid Iterative Scheme for Nonexpensive Mappings and Applications by Jie Jia, Khurram Shabbir, Khushdil Ahmad, Nehad Ali Shah, Thongchai Botmart

“…By using the Picard-Thakur hybrid iterative scheme, we can find the solution of delay differential equations and also prove some convergence results for nonexpansive mapping in a uniformly convex Banach space.…”
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Almost Sure Stability of Stochastic Neural Networks with Time Delays in the Leakage Terms by Mingzhu Song, Quanxin Zhu, Hongwei Zhou

“…By using the LaSalle invariant principle of stochastic delay differential equations, Itô’s formula, and stochastic analysis theory, some novel sufficient conditions are derived to guarantee the almost sure stability of the equilibrium point. …”
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Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays by Fulgensia Kamugisha Mbabazi, Joseph Y. T. Mugisha, Mark Kimathi

“…The stability theory of delay differential equations is used to analyze the model. The results show that the disease-free equilibrium is asymptotically stable if the control reproduction ratio R0 is less than unity and unstable otherwise. …”
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Z2×Z3 Equivariant Bifurcation in Coupled Two Neural Network Rings by Baodong Zheng, Haidong Yin

“…We discuss the spatiotemporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay differential equations combined with representation theory of Lie groups. …”
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A simple model of carcinogenic mutations with time delay and diffusion by Monika Joanna Piotrowska, Urszula Foryś, Marek Bodnar, Jan Poleszczuk

“…In the paper we consider a system of delay differential equations (DDEs) of Lotka-Volterra type with diffusion reflecting mutations from normal to malignant cells. …”
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Positivity of Fundamental Matrix and Exponential Stability of Delay Differential System by Alexander Domoshnitsky, Roman Shklyar, Mikhail Gitman, Valery Stolbov

“…Results on nonnegativity of the Cauchy matrix for system of delay differential equations xi′t+∑j=1n‍pijtxjhijt=fit,   i=1,…,n, which were based on nonpositivity of all diagonal elements, were presented in the previous works. …”
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Improving diversification by a hybrid bat-Nelder-Mead algorithm and DDE for rapid convergence to solve global optimization by Enas Suhail, Mahmoud El-Alem, Omar Bazighifan, Ahmed Zekri

“…Delay differential equations and algorithms hold a crucial position in the exploration of some biological systems and several models in real-world applications. …”
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Bifurcation and controller design in a 3D delayed predator-prey model by Jinting Lin, Changjin Xu, Yiya Xu, Yingyan Zhao, Yicheng Pang, Zixin Liu, Jianwei Shen

“…This paper determines the parameter conditions for system stability and the occurrence of bifurcations by employing bifurcation theory and the stability theory of delayed differential equations. Using two control strategies, namely the mixed controller and the extended delay feedback controller, this paper effectively adjusts the stability domain of the delayed predator-prey systems and controls the time of bifurcation onset. …”
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A Fuzzy Delay Approach for HIV Dynamics Using a Cellular Automaton by R. Motta Jafelice, C. A. F. Silva, L. C. Barros, R. C. Bassanezi

“…The objective of this research is to study the evolution of CD4+ T lymphocytes infected with HIV in HIV-seropositive individuals under antiretroviral treatment utilizing a mathematical model consisting of a system of delay-differential equations. The infection rate of CD4+ T lymphocytes is a time-dependent parameter with delay. …”
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Artificial neural networks for stability analysis and simulation of delayed rabies spread models by Ramsha Shafqat, Ateq Alsaadi

“…This study addressed the complexity of rabies spread by integrating two critical delay effects—vaccination efficacy and incubation duration—into a delay differential equations model, capturing more realistic infection patterns between dogs and humans. …”
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Reconstruction of self-oscillating systems with delay time modulation by Ponomarenko, Vladimir Ivanovich, Prokhorov, Mihail Dmitrievich

“…The object of study is self-oscillating systems described by delay-differential equations, in which the delay time is modulated by an external periodic signal. …”
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The Effect of Delay Techniques on a Lassa Fever Epidemic Model by Ali Raza, Eugenio Rocha, Emad Fadhal, Rashid I. H. Ibrahim, Eman Afkar, Muhammad Bilal

“…By introducing a delay parameter and decay exponential term into the existing model in the literature, we got the system of highly nonlinear delay differential equations (DDEs). The fundamental properties such as positivity, boundedness, existence, and uniqueness are verified for the said model. …”
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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. …”
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Bifurcation analysis of multistability and hysteresis in a model of HIV infection by I. V. Mironov, M. Yu. Khristichenk, Yu. M. Nechepurenko, D. S. Grebennikov, G. A. Bocharov

“…To this end, original computational methods of bifurcation analysis of mathematical models formulated with systems of ordinary differential equations and delay differential equations are used. The macrophage activation rate constant is considered as a bifurcation parameter. …”
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