Travelling fronts for the KPP equation with spatio-temporal delay

By Peter Ashwin, M. Bartuccelli, Thomas J. Bridges, Stephen A. Gourley. 2002

135 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Numerical Analysis, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/a0301a46798911386337e23dc4c6e0adbafbca93

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Citations in the corpus

Bistable wavefronts in a diffusive and competitive Lotka-Volterra type system with nonlocal delays (2008, background): “Thus, the regularity of u3 and u4 is clear, it refers to [1,4,18].”
Wavefronts and global stability in a time-delayed population model with stage structure (2003, result): “This is in contrast to analytical and numerical studies of other delay and non-local reaction{ di¬usion equations, which can have non-monotone fronts for su¯ ciently large delays (see, for example, Ashwin et al. 2002; Gourley 2000a; b; So et al .”
Travelling wave fronts in reaction-diffusion systems with spatio-temporal delays (2006, methodology): “[2] considered the same case as that we consider in Case 3.”
Traveling Fronts in Monostable Equations with Nonlocal Delayed Effects (2008, background): “[4], Gourley and Ruan [21], Ruan and Xiao [36], etc.”
The non-local Fisher–KPP equation: travelling waves and steady states (2009, methodology): “3 (with μ replaced by τμ) show that the operator Fτ does not vanish on the boundary ∂BK with K sufficiently large for any τ ∈ [0, 1].”
Monotone traveling wavefronts of the KPP-Fisher delayed equation (2010, background): “C A ] 2 0 In the early 2000’s, Gourley (2000), Wu et al. (2001), Ashwin et al. (2002) initiated the study of the positive wavefronts in the delayed Kolmogorov-Petrovskii-PiskunovFisher equation ut(t, x) = ∆u(t, x) + u(t, x)(1 − u(t− h, x)), u ≥ 0, x ∈ Rm. (∗) Since then, this model has become one…”
Travelling wave fronts in nonlocal delayed reaction-diffusion systems and applications (2009, background): “Since then, the theory of reaction-difiusion equations attracts much attention due to its signiflcant nature in mathematical theory and practical flelds, see, e.g., Ashwin et al. [ 1 ], Britton [5], Li and Wang [24], Murray [28], Smoller [33], Wang et al. [37, 38], Wu [39], Ye and Li [42].”
Periodic travelling waves in cyclic predator–prey systems (2001, background): “…the rate of invasion is determined by predator characteristics only, the cyclic nature of the interaction with prey leads to either periodic travelling waves or spatiotemporal chaos behind invasion (Sherratt et al. 1995, 1997; Petrovskii & Malchow 1999; Ashwin et al. 2000; see also Pascual 1993).”
Delay induced traveling wave fronts in reaction diffusion equations of KPP-Fisher type (2002, background): “[1] show that the wave fronts will lose monotonicity and develop oscillations on the lee-side of the front.”
Nonlocality of Reaction-Diffusion Equations Induced by Delay: Biological Modeling and Nonlinear Dynamics (2004, background): “, 30 (1978), 33–76 MathSciNet Zentralblatt MATH [6] Ashwin P.”