Wavefronts and global stability in a time-delayed population model with stage structure

By Yang Kuang, Stephen A. Gourley. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2003

174 citations recorded by the source corpus.

Subfields: Genetics, Public Health, Environmental and Occupational Health, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/fe04bc3d4e20ade6b812fc34529ee825e6b577fb

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Citations in the corpus

Nonmonotone travelling waves in a single species reaction–diffusion equation with delay (2005, result): “As it was noticed in [1,9, 10 ,12,20,29], various investigators have studied numerically the case of a large delay in the Nicholson’s blowflies equation, and noted a loss of monotonicity of the wave front as the delay increases, “with the front developing a prominent hump” whose height “is bounded a”
Traveling waves for non-local delayed diffusion equations via auxiliary equations☆ (2007, unknown): “(1.2), the following reaction–diffusion equation wt(t, x) = Dwxx(t, x) − βw2(t, x) + αe−γ r ∫ R 1√ 4πdr e− (x−y)2 4dr w(t − r, y) dy (1.6) with β > 0, d 0, α > 0 and r 0, was also proposed by Gourley and Kuang [4] to describe the evolution of the mature population of a single species population with”
Traveling wavefronts for time-delayed reaction-diffusion equation: (II) Nonlocal nonlinearity (2009, methodology): “For research related to other models of population dynamics, we refer to [1–3,5,6,11–13,16] and the references therein.”
Bistable wavefronts in a diffusive and competitive Lotka-Volterra type system with nonlocal delays (2008, background): “[25] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston, 1993.”
Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models (2003, methodology): “7) reduces to the model discussed in [15].”
Traveling wave fronts for generalized Fisher equations with spatio-temporal delays (2007, unknown): “See [1,3,4,9,12–14,16,19,21,23–27] and the references therein.”
On the existence of traveling waves for delayed reaction–diffusion equations☆ (2009, background): “[7] S.A. Gourley, Y. Kuang, Wavefronts and global stability in a time-delayed population model with stage structure, Proc.”
A non-local PDE model for population dynamics with state-selective delay: Local theory and global attractors (2006, result): “Recent development leads to a new class of reaction–diffusion equations with the nonlinear reaction terms involving non-local (in space) and delayed (in time) nonlinearities, we refer this to the earlier work of Smith and Thieme [44], Britton [7], and Gourley and Britton [22], Gourley and Kuang [23]”
Geometric stability switch criteria in delay differential equations with two delays and delay dependent parameters (2019, background): “1) increases rapidly as rτ passes through π/2, leading to solutions with extremely large maximum value, and a minimum close to zero (see Figure 1 in [13]).”
Existence and uniqueness of traveling waves for non-monotone integral equations with applications (2010, background): “1) reduces to the model studied in [21], which is a generalization of the model derived in [18] (see also [10]); when g(u) = du, (4.”
Traveling wave solutions in delayed reaction diffusion systems with applications to multi-species models (2009, background): “In particular, the traveling wave solution is one of the most attracted objects in investigating the dynamical properties of delayed evolution systems due to its significant applications in theory and applications, such as in describing the transition between different states of a physical system an”
Travelling wave fronts in reaction-diffusion systems with spatio-temporal delays (2006, background): “Since then, great progress has been made on the existence of travelling wave fronts in reaction–diffusion equations with spatio-temporal delays, see [1–3,9,10, 12–16,21,25,28,30,35].”
Diffusive and nondiffusive population models (2010, methodology): “More elaborate models have been proposed by Gourley and Kuang [54].”