To illustrate the formation and stability of wave solutions we turn our attention to a
class of nonlocal delayed RD equation proposed by So et al (2001, Proc. R. Soc.
Lond. A, 457, 1841–1853). In particular, the
authors adopted Smith-Thieme’s approach to obtain the following model of single
species population.
where x ∈ R, 0 <
ε≤ 1, w(x, t) represents the total mature population u(x, a, t) at age
a, time t and position x that is given by
The kernel function is given by
Formation of the traveling waves of the model with constant delay (τ
= 12)
Formation of traveling waves with Gibbs phenomenon due to increasing
delay
PDE solution for
τ = 11
Formation of a wavefront in a 2-dimensional domain
for the reduced model