Transient Dynamics on the Edge of Stability

Part of the Nonlinear Systems and Complexity book series (NSCH, volume 12)


Here we propose, on the basis of the winnerless competition (WLC) principle, which induces robust transient dynamics in open complex networks, and whose geometrical image in phase space is a heteroclinic sequence, to study the behavior of complex multiagent systems such as brain or ecological food networks that present transient dynamics in a network with active elements whose equilibria are in multidimensional unstable manifolds. In particular, we introduce and study numerically a characteristic of sequential transient dynamics, an uncertainty function that measures the level of nonreproducibility of generalized heteroclinic channels. For a Lotka–Volterra-type model, we describe the behavior of uncertainty functions and its dependence on parameters of the system. We analyze the probability to get a heteroclinic chain with fixed uncertainty and its dependence on the number of saddles of the chain and the number of elements in the network.



We thank Valentin Afraimovich for many constructive discussions and suggestions that helped us to make this piece of research stronger. I.T. acknowledges support by CONACYT. M.R. was supported by US Naval Research by grant ONR N00014-1-0741.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Instituto de Investigacion en Comunicacion OpticaUniversidad Autonoma de San Luis PotosiSan Luis PotosiMexico
  2. 2.BioCircuits InstituteUniversity of California San DiegoLa JollaUSA

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