1,533 research outputs found
Evolutionary modeling in economics : recent history and immediate prospects
Abstract not availablemathematical economics and econometrics ;
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Robust permanence for ecological equations with internal and external feedbacks.
Species experience both internal feedbacks with endogenous factors such as trait evolution and external feedbacks with exogenous factors such as weather. These feedbacks can play an important role in determining whether populations persist or communities of species coexist. To provide a general mathematical framework for studying these effects, we develop a theorem for coexistence for ecological models accounting for internal and external feedbacks. Specifically, we use average Lyapunov functions and Morse decompositions to develop sufficient and necessary conditions for robust permanence, a form of coexistence robust to large perturbations of the population densities and small structural perturbations of the models. We illustrate how our results can be applied to verify permanence in non-autonomous models, structured population models, including those with frequency-dependent feedbacks, and models of eco-evolutionary dynamics. In these applications, we discuss how our results relate to previous results for models with particular types of feedbacks
Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations
Finite-size fluctuations in coevolutionary dynamics arise in models of
biological as well as of social and economic systems. This brief tutorial
review surveys a systematic approach starting from a stochastic process
discrete both in time and state. The limit of an infinite
population can be considered explicitly, generally leading to a replicator-type
equation in zero order, and to a Fokker-Planck-type equation in first order in
. Consequences and relations to some previous approaches are
outlined.Comment: Banach Center publications, in pres
The conflict interaction between two complex systems. Cyclic migration
We construct and study a discrete time model describing the conflict
interaction between two complex systems with non-trivial internal structures.
The external conflict interaction is based on the model of alternative
interaction between a pair of non-annihilating opponents. The internal conflict
dynamics is similar to the one of a predator-prey model. We show that the
typical trajectory of the complex system converges to an asymptotic attractive
cycle. We propose an interpretation of our model in terms of migration
processes
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