Routes to extreme events in dynamical systems: Dynamical and statistical characteristics

Arindam Mishra, S. Leo Kingston, Chittaranjan Hens, Tomasz Kapitaniak, Ulrike Feudel, Syamal K. Dana

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


Intermittent large amplitude events are seen in the temporal evolution of a state variable of many dynamical systems. Such intermittent large events suddenly start appearing in dynamical systems at a critical value of a system parameter and continues for a range of parameter values. Three important processes of instabilities, namely, interior crisis, Pomeau-Manneville intermittency, and the breakdown of quasiperiodic motion, are most common as observed in many systems that lead to such occasional and rare transitions to large amplitude spiking events. We characterize these occasional large events as extreme events if they are larger than a statistically defined significant height. We present two exemplary systems, a single system and a coupled system, to illustrate how the instabilities work to originate extreme events and they manifest as non-trivial dynamical events. We illustrate the dynamical and statistical properties of such events.

Original languageEnglish
Article number063114
Issue number6
StatePublished - 1 Jun 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2020 Author(s).


T.K. and S.L.K. have been supported by the National Science Centre, Poland, OPUS program (Project No. 2018/29/B/STB/00457). S.K.D. is supported by the Division of Dynamics, Lodz University of Technology, Poland. C.H. is supported by the INSPIRE-Faculty grant (Code No. IFA17-PH193). A.M. is supported by the CSIR (India). U.F. has been supported by the Volkswagen Foundation (Grant No. 88459).

FundersFunder number
Division of Dynamics
Council of Scientific and Industrial Research, India
Volkswagen Foundation88459
Narodowe Centrum Nauki2018/29/B/STB/00457
Politechnika LódzkaIFA17-PH193


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