Effects of predation efficiencies on the dynamics of a tritrophic food chain
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1.
Dipartimento di Matematica, Università di Milano, via Saldini 50, 20133 Milano
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2.
Dipartimento di Matematica, Università di Parma, V.le G.P. Usberti 53/A, 43100 Parma
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3.
Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino
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Received:
01 July 2006
Accepted:
29 June 2018
Published:
01 May 2007
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MSC :
92D25, 34C23.
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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.
Citation: Maria Paola Cassinari, Maria Groppi, Claudio Tebaldi. Effects of predation efficiencies on the dynamics of a tritrophic food chain[J]. Mathematical Biosciences and Engineering, 2007, 4(3): 431-456. doi: 10.3934/mbe.2007.4.431
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Abstract
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.
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