SELF-ORGANIZED STOCHASTIC TIPPING IN SLOW-FAST DYNAMICAL SYSTEMS

Mathias Linkerhand (1) , Claudius Gros (1)

1 institute for theoretical physics

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 quasi periodic 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.

Mots clés: stochastic tipping; complex systems; chaos; intrinsic adaption; slow-fast; metalearning

Domaines: Mécanique [physics.med-ph]

Mathias Linkerhand, Claudius Gros. SELF-ORGANIZED STOCHASTIC TIPPING IN SLOW-FAST DYNAMICAL SYSTEMS. Mathematics and Mechanics of Complex Systems, 2013, 1 (2), pp.129-147. ⟨10.2140/memocs.2013.1.129⟩. ⟨hal-00905610⟩