Delay Differential Equations: With Applications in Population Dynamics

By Yang Kuang. 2012

2,801 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7f4ed545e21fa29fa6f8244b92daa58eee9f0f72

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1. Meng Liu
2. Ke Wang
3. Jianhai Bao
4. Qi An
5. Junping Shi
6. Shanshan Chen
7. Chenggui Yuan
8. Xuerong Mao

Citations in the corpus

• Persistence and extinction in stochastic non-autonomous logistic systems (2011, unknown): “Freedman and Wu [2], Golpalsamy [3], Kuang [4], Lisena [5] and the references therein.”
• Delay-induced chaos and its possible control in a seasonally forced eco-epidemiological model with fear effect and predator switching (2021, background): “In the realistic scenario, the dynamical behaviours of a system, such as, digestion of food [30], prey hunting [31], inducible defence in prey population [32], disease transmission [33], etc.”
• Population dynamical behavior of a two-predator one-prey stochastic model with time delay (2017, background): “Mathematical and ecological results have shown that time delay should not be neglected ([11, 20]) and population models with three-species are more appropriate than single-species models and two-species models ([13, 40]), therefore we pay attention to a two-predator one-prey stochastic model with ti”
• The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional brownian motion (2011, background): “, Hale and Verduyn Lunel [11] and Manitius [12]), or biological motivations like species growth or incubating time in disease models among many others (see Kuang [10] and Murray [15], for instance).”
• Geometric stability switch criteria in delay differential equations with two delays and delay dependent parameters (2019, background): “This is also clear for the Hutchinson model where small positive solutions tend to the carrying capacity when rτ < π/2 [2].”
• Competitive Lotka–Volterra population dynamics with jumps (2011, background): “2) and here we only mention Gopalsamy [1], Kuang [2], Li et al.”
• Hopf bifurcation and stability for predator–prey systems with Beddington–DeAngelis type functional response and stage structure for prey incorporating refuge (2016, background): “The existed literature [1] had shown that a time delay could destroy the stability of the positive equilibrium and caused the fluctuation of population, thereby caused Hopf bifurcation.”
• Periodic solutions for a non-monotone family of delayed differential equations with applications to Nicholson systems (2016, background): “[15]) will always refer to the choice of C0 as the set of admissible initial conditions, given, as convention, at the instant of time t = 0: i.”
• Higher order numerical approximation for time dependent singularly perturbed differential‐difference convection‐diffusion equations (2018, background): “Some applications are the mathematical modeling of population dynamics and epidemiology [2], physiological kinetics [3], blood cell production [4], chemical kinetics [5], immune response [6], system involving a feedback control [1], and so forth.”
• Population dynamical behavior of Lotka-Volterra cooperative systems with random perturbations (2012, background): “In fact, owing to its theoretical and practical significance, system (1) has been extensively studied, and we here mention [1, 2, 3, 9, 10, 12, 15, 17, 19, 26, 27, 31, 33, 35, 36] among others.”