BookchapterYear:  2004 

Author(s):  HernandezGarcia, Emilio; Lopez, Cristobal 

Title:  Logistic population growth and beyond: the influence of advection and nonlocal effects 

Book title:   

Editorial:  SpringerVerlag 

ISBN:  

Abstract:  By introducing the logistic equation in the context of demographic
modelling, J.F. Verhulst made seminal
contributions to at least two important fields of research: The quantitative approach to Population Dynamics, and the basics of
Nonlinear Science.
The dynamics of biological populations in aquatic environments is an excellent framework to see recent developments in which these disciplines work together.
In this contribution we present two examples in the above field.
In both cases a prominent role is played by the logistic growth
process (i.e. population growth limited by finite resources), but
other ingredients are also included that strongly change the
phenomenology. First, a phytoplankton population
experiencing logistic growth is studied, but in interaction with
zooplankton predators that maintain it in a state below the
carrying capacity of the supporting medium. In the appropriate
parameter regime the system behaves in an excitable way, with
perturbations inducing large excitationdeexcitation cycles of the
phytoplankton population. The excitation cycles become strongly
affected by the presence of chaotic motion of the fluid containing
the populations.
Second, an individual based model of interacting organisms is
presented, for which logistic growth is again the main ingredient.
Reproduction of a given individual is limited by the presence of
others in a neighborhood of finite size. This nonlocal character of the interaction is enough to produce an instability
of the basic state of particles homogenously distributed, and
clustering of the individuals occurs, which form groups arranged
in an hexagonal lattice (when the population lives in a
twodimensional space). 


