# Veröffentlichungen

### 2019

Marwan, Norbert; Kraemer, Kai Hauke; Wiesner, Karolin; Breitenbach, Sebastian F. M.; Leonhardt, Jens

Recurrence based entropies Vortrag

07.05.2019, (Fourth International Conference on Recent Advances in Nonlinear Mechanics, Łódz (Poland)).

Abstract | BibTeX | Schlagwörter: bb-1, bb-3, entropy, northumbria, palaeoclimate, pik, stalagmite

@misc{marwan2019lodz,

title = {Recurrence based entropies},

author = {Norbert Marwan and Kai Hauke Kraemer and Karolin Wiesner and Sebastian F. M. Breitenbach and Jens Leonhardt},

editor = {Fourth International Conference on Recent Advances in Nonlinear Mechanics, Łódz (Poland)},

year = {2019},

date = {2019-05-07},

abstract = {Many dynamical processes are considered to be of complex nature. To get a quantitative idea of the complexity, often the Shannon entropy of the value distribution of a measurement is used. Alternative entropy measures have been suggested using the recurrence plot (RP) approach. A RP is a matrix that represents the recurrences of states in the d-dimensional phase space. The RP can consist of small-scale structures, such as single points, diagonal and vertical lines, which characterize important dynamical properties of the system. Various entropy measures have been defined using different features of the RP or can be related to certain properties of the RP. Because of the different features that are used, some entropy measures represent different aspects of the analysed system and, thus, behave differently. This fact can lead to misunderstandings and difficulties in interpreting and understanding those measures. We discuss definitions, motivation and interpretation of some of those entropy measures, compare their differences and discuss some of the pitfalls when using them. },

note = {Fourth International Conference on Recent Advances in Nonlinear Mechanics, Łódz (Poland)},

keywords = {bb-1, bb-3, entropy, northumbria, palaeoclimate, pik, stalagmite},

pubstate = {published},

tppubtype = {presentation}

}

Many dynamical processes are considered to be of complex nature. To get a quantitative idea of the complexity, often the Shannon entropy of the value distribution of a measurement is used. Alternative entropy measures have been suggested using the recurrence plot (RP) approach. A RP is a matrix that represents the recurrences of states in the d-dimensional phase space. The RP can consist of small-scale structures, such as single points, diagonal and vertical lines, which characterize important dynamical properties of the system. Various entropy measures have been defined using different features of the RP or can be related to certain properties of the RP. Because of the different features that are used, some entropy measures represent different aspects of the analysed system and, thus, behave differently. This fact can lead to misunderstandings and difficulties in interpreting and understanding those measures. We discuss definitions, motivation and interpretation of some of those entropy measures, compare their differences and discuss some of the pitfalls when using them.

Marwan, Norbert; Kraemer, Kai Hauke; Wiesner, Karolin; Breitenbach, Sebastian F. M.; Leonhardt, Jens

Recurrence based entropies Konferenzbeitrag

In: Geophysical Research Abstracts, S. EGU2019-2817, 2019.

Abstract | Links | BibTeX | Schlagwörter: bb-1, bb-3, entropy, northumbria, palaeoclimate, pik, stalagmite

@inproceedings{marwan2019,

title = {Recurrence based entropies},

author = {Norbert Marwan and Kai Hauke Kraemer and Karolin Wiesner and Sebastian F. M. Breitenbach and Jens Leonhardt},

url = {https://bbh.pik-potsdam.de/wp-content/uploads/2021/04/EGU2019-2817.pdf},

year = {2019},

date = {2019-04-08},

booktitle = {Geophysical Research Abstracts},

volume = {21},

pages = {EGU2019-2817},

abstract = {Dynamical processes in Earth sciences are often considered to be of complex nature. The term complexity is often used for processes that are either unpredictable (e.g. nonlinear dynamics), consist of many different components, or exhibit regime transitions (e.g. tipping points). To measure complexity, the Shannon entropy is often used.

Here we present various entropy measures that have been defined on the base of the recurrence plot. Because of the different features that are used, these entropy measures represent different aspects of the analysed system and, thus, behave differently. In the past, this fact has lead to difficulties in interpreting and understanding those measures. We summarize the definitions, the motivation and interpretation of these entropy measures, compare their differences and discuss some of the pitfalls when using them.

Finally, we illustrate their potential in an application on palaeoclimate time series. Using entropy measures, changes and transitions in the climate dynamics in the past can be identified and interpreted.},

keywords = {bb-1, bb-3, entropy, northumbria, palaeoclimate, pik, stalagmite},

pubstate = {published},

tppubtype = {inproceedings}

}

Dynamical processes in Earth sciences are often considered to be of complex nature. The term complexity is often used for processes that are either unpredictable (e.g. nonlinear dynamics), consist of many different components, or exhibit regime transitions (e.g. tipping points). To measure complexity, the Shannon entropy is often used.

Here we present various entropy measures that have been defined on the base of the recurrence plot. Because of the different features that are used, these entropy measures represent different aspects of the analysed system and, thus, behave differently. In the past, this fact has lead to difficulties in interpreting and understanding those measures. We summarize the definitions, the motivation and interpretation of these entropy measures, compare their differences and discuss some of the pitfalls when using them.

Finally, we illustrate their potential in an application on palaeoclimate time series. Using entropy measures, changes and transitions in the climate dynamics in the past can be identified and interpreted.

Here we present various entropy measures that have been defined on the base of the recurrence plot. Because of the different features that are used, these entropy measures represent different aspects of the analysed system and, thus, behave differently. In the past, this fact has lead to difficulties in interpreting and understanding those measures. We summarize the definitions, the motivation and interpretation of these entropy measures, compare their differences and discuss some of the pitfalls when using them.

Finally, we illustrate their potential in an application on palaeoclimate time series. Using entropy measures, changes and transitions in the climate dynamics in the past can be identified and interpreted.