Singular homoclinic bifurcations in tritrophic food chains
نویسندگان
چکیده
منابع مشابه
Belyakov Homoclinic Bifurcations in a Tritrophic Food Chain Model
Complex dynamics of the most frequently used tritrophic food chain model are investigated in this paper. First it is shown that the model admits a sequence of pairs of Belyakov bifurcations (codimension-two homoclinic orbits to a critical node). Then fold and period-doubling cycle bifurcation curves associated to each pair of Belyakov points are computed and analyzed. The overall bifurcation sc...
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1. Introduction. We say that a one-parameter family of diffeomorphisms ip^: M — • M, p G R, has a homoclinic bifurcation, or a homoclinic tangency, for p = 0 if ipo has an orbit of nontransverse intersection of a stable and an unstable manifold, both of the same hyperbolic fixed point (or periodic point), which splits, for p > 0, into two orbits of transverse intersection of these stable and un...
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Nonlinear models and laboratory experiments suggest that populations can be chaotic, whereas field data show that a fair proportion of observed populations are not too far from being chaotic. Thus, a natural question arises: do ecosystems enjoy special properties at the edge of chaos? By limiting the analysis to three classes of tritrophic food chains and to the role played by the nutrient avai...
متن کاملBifocal homoclinic bifurcations
Homoclinic orbits to bifocus-type stationary points have been studied theoretically by a number of authors, but up until now, only one analytic example has been found. In this paper we summarise and extend the known theory regarding bifocal homoclinic bifurcations and present numerical verification of some of the more interesting theoretical predictions that have been made.
متن کاملImperfect homoclinic bifurcations.
Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics observed in the circuit can be understood by reference to imperfect homoclinic bifurcations without constructing an explicit mathematical model of the system.
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ژورنال
عنوان ژورنال: Mathematical Biosciences
سال: 1998
ISSN: 0025-5564
DOI: 10.1016/s0025-5564(97)10001-3