Bifurcation and singularities in models of biosystems

Dynamic regimes and bifurcations in the compartment model of carbon cycle functioning in a mesotrophic bog ecosystem Nicolai N. Zavalishin1 . Complexity of structure and nonlinearity of functioning are key features of ecosystems that are represented by ”storage-flow” diagrams reflecting matter or energy cycling between ecosystem components at fixed times. Using the data from diagrams aggregated in ecological field studies, one can construct a dynamic compartmental model of the ecosystem to predict future behaviour and to estimate a response to external perturbations. Svirezhev’s method of a dynamic model design by a balanced ”storageflow” diagram is based on simple physical assumptions and appears to be one of most effective in modelling ecosystem dynamics. This approach is applied for investigating dynamic regimes of carbon cycle functioning in a southern taiga mesotrophic bog ecosystem (Tajozhny Log, Novgorod Region, Russia). Among the most urgent problems related to estimating the consequences of greenhouse effect, are the reaction of terrestrial ecosystems to an increase of atmospheric carbon concentration and the possibility for them to compensate that increase by means of disposal carbon input. Therefore asymptotic stability of both current equilibrium and possible alternative equilibrium states as well as more complicated attractors are studied concerning two types of parameter perturbations: atmospheric carbon concentration increase and change in the rate of carbon output from dead organic matter and litter due to human activities. For the dynamic model based on the flow-balanced compartment scheme consisting of four most meaningful carbon pools of the bog, three ecologically interpretable equilibria are obtained: a transformed ecosystem,

Bifurcation and singularities in models of biosystems

a forest and a raised bog. Calculation of bifurcation curves shows areas in the parameter space where stable functioning of carbon cycle is provided. The modern equilibrium loses its stability under increase of carbon assimilation by plants with appearing of oscillatory dynamics and further evolution to a chaotic attractor. This results in a limited capacity of bog ecosystems to compensate an increase of carbon input from the atmosphere without loss of stability. Critical values for carbon pressure corresponding to bifurcation points are obtained. It is shown that chaotic oscillations can be considered as transitional regimes between different ecologically interpretable stable configurations of carbon cycle.

1

Laboratory of mathematical ecology, Institute of atmospheric physics RAS, 3, Pyzhevsky Lane, 119017, Moscow, Russia (e-mail: [email protected]; [email protected]).

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AICME II abstracts

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