Symbolic Toolkit for Chaos Explorations
نویسندگان
چکیده
Computational technique based on the symbolic description utilizing kneading invariants is proposed 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.
منابع مشابه
Kneadings, Symbolic Dynamics and Painting Lorenz Chaos
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 detects their organizing centers — codimension-two T-points and...
متن کاملHomoclinic Spirals: Theory and Numerics
In this paper we examine spiral structures in bi-parametric diagrams of dissipative systems with strange attractors. First, we show that the organizing center for spiral structures in a model with the Shilnikov saddle-focus is related to the change of the structure of the attractor transitioning between the spiral and screw-like types located at the turning point of a homoclinic bifurcation cur...
متن کاملNonlinear dynamics and chaos in information processing neural networks
We consider a number of possible roles of complex dynamics and chaos in information processing by neural networks. First, we review the working principles of some well-known neural networks, and then discuss a number of approaches to utilization of chaos in neural networks. Our main goal is to present a novel view of the problem of chaos in information processing. We demonstrate that chaos emer...
متن کاملApplications of Symbolic Dynamics in Chaos Synchronization
We give the relationship between symbolic dynamics and chaos synchronization. If the capacity of the channel which onedirectionally connects two chaotic systems with the aim of synchronizing them is larger than Kolmogorov–Sinai entropy of the driving system, then the synchronization error can be made arbitrarily small.
متن کاملSymbolic Automata: The Toolkit
The symbolic automata toolkit lifts classical automata analysis to work modulo rich alphabet theories. It uses the power of stateof-the-art constraint solvers for automata analysis that is both expressive and efficient, even for automata over large finite alphabets. The toolkit supports analysis of finite symbolic automata and transducers over strings. It also handles transducers with registers...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013