Chaos: An Ecological Reality?

Upadhyay, Ranjit Kumar; Iyengar, S. R. K.; Rai, Vikas

doi:10.1142/s0218127498001029

Cited by 82 publications

(36 citation statements)

References 19 publications

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“…Although ecological models were among the first examples of chaos, 35 it was often argued that chaos should disappear when more ecological details are taken into account. 36,37 By application of generalized models it has been shown that double Hopf bifurcations generally exist in food chains with more than three trophic levels.…”

Section: Some Results On Global Dynamicsmentioning

confidence: 99%

Generalized models – A new tool for the investigation of ecological systems

Groß

Baurmann

Feudel

et al. 2007

Complex Population Dynamics

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Ecological systems are commonly studied by very concrete conventional models or very abstract random matrix models. Here we review and extend the approach of generalized structural kinetic modeling, that offers an intermediate way between these extremes. Generalized models describe systems with a specific structure, but do not restrict the processes in the model to specific functional forms. The approach is based on the construction of a locally linear model in every point of parameter space, in such a way that each element of the model is directly accessible to measurement and has a well defined ecological interpretation. Here we show that generalized models can be used to study the local asymptotic stability of steady states and reveal certain features of the global dynamics. Among other examples we present results on spatial predator-prey system and a complex food web.

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Section: Some Results On Global Dynamicsmentioning

confidence: 99%

Generalized models – A new tool for the investigation of ecological systems

Groß

Baurmann

Feudel

et al. 2007

Complex Population Dynamics

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“…Predatorprey interaction is the most common. There are two types of predators: (i) specialists and (ii) generalists [8][9][10][11][12][13][14][15][16][17][18][19][20]. A specialist predator feeds only one food.…”

Section: Specialist and Generalist Predators Our Modelmentioning

confidence: 99%

Bifurcation Analysis for Metapopulation Models

Kara

2012

scjournal

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Two models with four components of chain populations are considered. In the model, a prey population X is predated by individuals of a specialist predator population Y, and another prey population Z is predated by individuals of a generalist predator population U. This model is governed by a system of four nonlinear first order ordinary differential equations. To study the dynamics of the food chain model, the mentioned system of ordinary differential equations solved numerically. One of the biological parameters varied in a sufficiently large range and its effects on the dynamics of the system are observed. Along the  w axis of the predating rate of the specialist predator Y , around four points

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“…One question that has been discussed in the ecological literature for quite some time is whether chaotic dynamics occur in natural food webs (May 1987;Upadhyay et al 1998;Rai and Schaffer 2001). On the one hand, even some of the simplest ecological models exhibit chaotic dynamics (e.g., May 1974May , 1976Edwards and Yool 2000).…”

Section: Equivalence Of More Complex Food Websmentioning

confidence: 99%

Local dynamical equivalence of certain food webs

Groß

Feudel

2008

Ocean Dynamics

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An important challenge in theoretical ecology is to find good coarse-grained representations of complex food webs. Here, we use the approach of generalized modeling to show that it may be possible to formulate a coarse-graining algorithm that conserves the local dynamics of the model exactly. We show examples of food webs with a different number of species that have exactly identical local bifurcation diagrams. Based on these observations, we formulate a conjecture governing which populations of complex food webs can be grouped together into a single variable without changing the local dynamics. As an illustration, we use this conjecture to show that chaotic regions generically exist in the parameter space of a class of food webs with more than three trophic levels. While our conjecture is at present only applicable to relatively special cases, we believe that its applicability could be greatly extended if a more sophisticated mapping of parameters were used in the model reduction.

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Chaos: An Ecological Reality?

Cited by 82 publications

References 19 publications

Generalized models – A new tool for the investigation of ecological systems

Generalized models – A new tool for the investigation of ecological systems

Bifurcation Analysis for Metapopulation Models

Local dynamical equivalence of certain food webs

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