Open AccessEffects of predation efficiencies on the dynamics of a tritrophic food chain
Author(s) -
Maria Paola Cassinari,
Maria Groppi,
Claudio Tebaldi
Publication year - 2007
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2007.4.431
Subject(s) - chaotic , limit (mathematics) , statistical physics , persistence (discontinuity) , food chain , hopf bifurcation , predation , dynamics (music) , functional response , bifurcation , complex dynamics , stability (learning theory) , predator , mathematics , limit cycle , control theory (sociology) , biological system , physics , ecology , biology , economics , computer science , control (management) , mathematical analysis , nonlinear system , acoustics , engineering , management , quantum mechanics , machine learning , geotechnical engineering
In this paper the dynamics of a tritrophic food chain (resource, consumer, top predator) is investigated, with particular attention not only to equilibrium states but also to cyclic behaviours that the system may exhibit. The analysis is performed in terms of two bifurcation parameters, denoted by p and q, which measure the efficiencies of the interaction processes. The persistence of the system is discussed, characterizing in the (p; q) plane the regions of existence and stability of biologically significant steady states and those of existence of limit cycles. The bifurcations occurring are discussed, and their implications with reference to biological control problems are considered. Examples of the rich dynamics exhibited by the model, including a chaotic regime, are described.