UCL  IRIS
Institutional Research Information Service
UCL Logo
Please report any queries concerning the funding data grouped in the sections named "Externally Awarded" or "Internally Disbursed" (shown on the profile page) to your Research Finance Administrator. Your can find your Research Finance Administrator at https://www.ucl.ac.uk/finance/research/rs-contacts.php by entering your department
Please report any queries concerning the student data shown on the profile page to:

Email: portico-services@ucl.ac.uk

Help Desk: http://www.ucl.ac.uk/ras/portico/helpdesk
Publication Detail
Manifolds of balance in planar ecological systems
Abstract
In the classic 2-species Lotka–Volterra competition model, and more general competitive planar Kolmogorov models, there is a continuous curve called the carrying simplex that links all non-zero steady states and attracts all non-zero population densities. This curve is where the opposing processes of population growth and decline balance. In this paper, we use stability analysis and index theory to show that such a curve also exists when the interactions between two species are more general, such as co-operative or predator-prey, provided that reasonable biologically motivated conditions hold. For example, both species experience intraspecific competition and all population densities remain bounded for all time. We consider systems where there is at most one co-existence steady state. The ‘balance manifold’ is formed of heteroclinic orbits and attracts all non-zero population densities, but unlike its competitive analogue, the curve is no longer necessarily continuously differentiable.
Publication data is maintained in RPS. Visit https://rps.ucl.ac.uk
 More search options
UCL Researchers
Author
Dept of Mathematics
University College London - Gower Street - London - WC1E 6BT Tel:+44 (0)20 7679 2000

© UCL 1999–2011

Search by