%0 Journal Article %1 PhysRevE.62.427 %A Cencini, M. %A Falcioni, M. %A Olbrich, E. %A Kantz, H. %A Vulpiani, A. %D 2000 %I American Physical Society %J Phys. Rev. E %K cencini chaos data-analysis noise nonlinear time-series %N 1 %P 427--437 %R 10.1103/PhysRevE.62.427 %T Chaos or noise: Difficulties of a distinction %V 62 %X In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set, it is not possible to reconstruct the invariant measure up to an arbitrarily fine resolution and an arbitrarily high embedding dimension. These restrictions limit our ability to distinguish between signals generated by different systems, such as regular, chaotic, or stochastic ones, when analyzed from a time series point of view. We propose to classify the signal behavior, without referring to any specific model, as stochastic or deterministic on a certain scale of the resolution ε, according to the dependence of the (ε,τ) entropy, h(ε, τ), and the finite size Lyapunov exponent λ(ε) on ε.

@article{PhysRevE.62.427, abstract = {In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set, it is not possible to reconstruct the invariant measure up to an arbitrarily fine resolution and an arbitrarily high embedding dimension. These restrictions limit our ability to distinguish between signals generated by different systems, such as regular, chaotic, or stochastic ones, when analyzed from a time series point of view. We propose to classify the signal behavior, without referring to any specific model, as stochastic or deterministic on a certain scale of the resolution ε, according to the dependence of the (ε,τ) entropy, h(ε, τ), and the finite size Lyapunov exponent λ(ε) on ε. }, added-at = {2007-10-05T00:31:13.000+0200}, author = {Cencini, M. and Falcioni, M. and Olbrich, E. and Kantz, H. and Vulpiani, A.}, biburl = {https://www.bibsonomy.org/bibtex/240406bf51e92469964c8988276778d8c/mcencini}, description = {Phys. Rev. E 62 (2000): M. Cencini, M. Falcioni, E. Olbrich, H. Kantz, and A. Vulpiani - Chaos or noise: Difficulties...}, doi = {10.1103/PhysRevE.62.427}, interhash = {bef0cc76e4121588be92cc53e1542aca}, intrahash = {40406bf51e92469964c8988276778d8c}, journal = {Phys. Rev. E}, keywords = {cencini chaos data-analysis noise nonlinear time-series}, month = Jul, number = 1, numpages = {10}, pages = {427--437}, publisher = {American Physical Society}, timestamp = {2007-10-05T00:47:28.000+0200}, title = {Chaos or noise: Difficulties of a distinction}, volume = 62, year = 2000 }