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Pattern formation in Malthusian growth with transport memory

S Harris

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We consider the effect of memory-dependent transport on the survivability of a population dispersing in a closed domain surrounded by a hostile environment. The model we use combines memory-dependent diffusion with Malthusian growth. The former introduces an additional parameter, the correlation time for memory effects, that must be taken into account in determining the critical length below which survival does not occur. Results are obtained for all possible parametric conditions, and the relevance to non-linear growth conditions is discussed.


PACS

05.45.-a Nonlinear dynamics and nonlinear dynamical systems

87.23.Cc Population dynamics and ecological pattern formation

MSC

92C15 Developmental biology, pattern formation

92D40 Ecology

Subjects

Environmental and Earth science

Statistical physics and nonlinear systems

Dates

Issue 30 (1 August 2003)

Received 16 April 2003

Published 16 July 2003



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