Majid Bani-Yaghoub, Ph.D.Associate Professor of Applied Mathematics
Office: Manheim 205 A
|
Numerical Simulations of a Nonlocal Delayed Reaction-Diffusion Model
1. Convergence of PDE solution to stationary wavefront
|
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
Impacts of the maturation time delay τ: (1) the PDE solution oscillatea in the spatial domain due to increased delay value. (2) the PDE solution converges to the trivial solution (i.e., the population goes extinct).
(1) PDE solution with birth function b(w) = p.w.exp(aw)
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
Impacts of the maturation time delay τ: (1) the PDE solution oscillatea in the spatial domain due to increased delay value. (2) the PDE solution converges to the trivial solution (i.e., the population goes extinct).
(1) PDE solution with birth function b(w) = p.w.exp(aw)
 PDE solution for τ=80  More simulations  (2) PDE solution with birth function b(w) = p.w^2.exp(aw)  More simulations  |