ISSN:
1432-1416
Keywords:
Retarded differential equations
;
Diffusion-instability
Source:
Springer Online Journal Archives 1860-2000
Topics:
Biology
,
Mathematics
Notes:
Abstract We analyze three simple population models that include generation times in their growth dynamics. In the presence of a slow one-dimensional diffusion process it is shown that for sufficiently small wave numbers, the amplitude of the homogeneous limit cycle solution is unstable and the phase of the bifurcating diffusion wave obeys a Burgers' type equation with a negative coefficient in the diffusion term. Numerical solutions for the phase and amplitude in the post-critical regime display a turbulent like behavior in space and time when the size of the system is larger than some critical value. This result follows from the coupling between the delay and diffusion terms.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00276071
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