196 research outputs found
Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial
A new computational technique based on the symbolic description utilizing
kneading invariants is proposed and verified for explorations of dynamical and
parametric chaos in a few exemplary systems with the Lorenz attractor. The
technique allows for uncovering the stunning complexity and universality of
bi-parametric structures and detect their organizing centers - codimension-two
T-points and separating saddles in the kneading-based scans of the iconic
Lorenz equation from hydrodynamics, a normal model from mathematics, and a
laser model from nonlinear optics.Comment: Journal of Bifurcations and Chaos, 201
Symbolic Toolkit for Chaos Explorations
New computational technique based on the symbolic description utilizing
kneading invariants is used for explorations of parametric chaos in a two
exemplary systems with the Lorenz attractor: a normal model from mathematics,
and a laser model from nonlinear optics. The technique allows for uncovering
the stunning complexity and universality of the patterns discovered in the
bi-parametric scans of the given models and detects their organizing centers --
codimension-two T-points and separating saddles.Comment: International Conference on Theory and Application in Nonlinear
Dynamics (ICAND 2012
Subthreshold oscillations in a map-based neuron model
Self-sustained subthreshold oscillations in a discrete-time model of neuronal
behavior are considered. We discuss bifurcation scenarios explaining the birth
of these oscillations and their transformation into tonic spikes. Specific
features of these transitions caused by the discrete-time dynamics of the model
and the influence of external noise are discussed.Comment: To be published in Physics Letters
A propensity criterion for networking in an array of coupled chaotic systems
We examine the mutual synchronization of a one dimensional chain of chaotic
identical objects in the presence of a stimulus applied to the first site. We
first describe the characteristics of the local elements, and then the process
whereby a global nontrivial behaviour emerges. A propensity criterion for
networking is introduced, consisting in the coexistence within the attractor of
a localized chaotic region, which displays high sensitivity to external
stimuli,and an island of stability, which provides a reliable coupling signal
to the neighbors in the chain. Based on this criterion we compare homoclinic
chaos, recently explored in lasers and conjectured to be typical of a single
neuron, with Lorenz chaos.Comment: 4 pages, 3 figure
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