Vol. 1, No. 2, 2013

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ISSN: 2325-3444 (e-only)
ISSN: 2326-7186 (print)
Self-organized stochastic tipping in slow-fast dynamical systems

Mathias Linkerhand and Claudius Gros

Vol. 1 (2013), No. 2, 129–147
Abstract

Polyhomeostatic adaption occurs when evolving systems try to achieve a target distribution function for certain dynamical parameters, a generalization of the notion of homeostasis. Here we consider a single rate-encoding leaky integrator neuron model driven by white noise, adapting slowly its internal parameters, threshold and gain, in order to achieve a given target distribution for its time-averaged firing rate. For the case of sparse encoding, when the target firing-rate distribution is bimodal, we observe the occurrence of spontaneous quasiperiodic adaptive oscillations resulting from fast transition between two quasistationary attractors. We interpret this behavior as self-organized stochastic tipping, with noise driving the escape from the quasistationary attractors.

Keywords
stochastic tipping, complex systems, chaos, intrinsic adaption, slow-fast, metalearning
Physics and Astronomy Classification Scheme 2010
Primary: 05.10.Gg, 05.40.Ca, 05.45.-a, 05.45.Tp, 05.65.+b
Milestones
Received: 4 April 2012
Revised: 13 July 2012
Accepted: 3 November 2012
Published: 16 April 2013

Communicated by Roberto Camassa
Authors
Mathias Linkerhand
Institute for Theoretical Physics
Goethe University
Max-von-Laue-Straße 1
D-60438 Frankfurt am Main
Germany
Claudius Gros
Institute for Theoretical Physics
Goethe University
Max-von-Laue-Straße 1
D-60438 Frankfurt am Main
Germany