The occurrence mechanisms of extreme events under random disturbances are relatively complex and not yet clear. In this paper, we take a class of generalized Duffing-type systems as an example to reveal three mechanisms for the occurrence of extreme events. First, it is intuitive that a very large excitation can generate extreme events, such as the Lévy noise. In such a case, extreme excitation works, while it does not require much about the systems. Second, when a system has a bifurcation structure, if the difference of the branches at the bifurcation point is large, a randomly varying bifurcation parameter can lead to extreme events. Finally, when a system has rare attractors, a random impulse excitation, such as Poisson white noise, is able to cause the system to escape from one general attractor into rare attractors. Such a kind of special regime switching behavior can lead to extreme events. These results reveal the possible mechanisms of extreme events in a class of nonlinear Duffing-type systems and provide guidance for further prediction and avoidance of extreme events.
REFERENCES
1.
A.
Volvach
, L.
Kogan
, K.
Kanonidi
, L.
Nadezhka
, I.
Bubukin
, V.
Shtenberg
, A.
Gordetsov
, O.
Krasnikova
, and D.
Kislitsyn
, “Changes in the properties of the statistics of physical and biophysical fields as earthquake precursor
,” Commun. Nonlinear Sci. Numer. Simul.
108
, 106200
(2022
). 2.
S.
Gupta
, N.
Boers
, F.
Pappenberger
, and J.
Kurths
, “Complex network approach for detecting tropical cyclones
,” Clim. Dyn.
57
, 3355
–3364
(2021
). 3.
J.
Zamora-Munt
, B.
Garbin
, S.
Barland
, M.
Giudici
, J. R. R.
Leite
, C.
Masoller
, and J. R.
Tredicce
, “Rogue waves in optically injected lasers: Origin, predictability, and suppression
,” Phys. Rev. A
87
(3
), 035802
(2013
). 4.
N.
Frolov
and A.
Hramov
, “Extreme synchronization events in a Kuramoto model: The interplay between resource constraints and explosive transitions
,” Chaos
31
(6
), 063103
(2021
). 5.
M.
Ghil
, P.
Yiou
, S.
Hallegatte
, B.
Malamud
, P.
Naveau
, A.
Soloviev
, P.
Friederichs
, V.
Keilis-Borok
, D.
Kondrashov
, V.
Kossobokov
, and O.
Mestre
, “Extreme events: Dynamics, statistics and prediction
,” Nonlinear Process. Geophys.
18
(3
), 295
–350
(2011
). 6.
G.
Ansmann
, R.
Karnatak
, K.
Lehnertz
, and U.
Feudel
, “Extreme events in excitable systems and mechanisms of their generation
,” Phys. Rev. E
88
(5
), 052911
(2013
). 7.
A.
Mishra
, S.
Leo Kingston
, C.
Hens
, T.
Kapitaniak
, U.
Feudel
, and S. K.
Dana
, “Routes to extreme events in dynamical systems: Dynamical and statistical characteristics
,” Chaos
30
(6
), 063114
(2020
). 8.
A.
Ray
, S.
Rakshit
, D.
Ghosh
, and S. K.
Dana
, “Intermittent large deviation of chaotic trajectory in Ikeda map: Signature of extreme events
,” Chaos
29
(4
), 043131
(2019
). 9.
J.
Spiechowicz
and J.
Łuczka
, “Arcsine law and multistable Brownian dynamics in a tilted periodic potential
,” Phys. Rev. E
104
(2
), 024132
(2021
). 10.
M.
Farazmand
and T. P.
Sapsis
, “Extreme events: Mechanisms and prediction
,” Appl. Mech. Rev.
71
(5
), 050801
(2019
). 11.
M. A.
Mohamad
and T. P.
Sapsis
, “Probabilistic description of extreme events in intermittently unstable dynamical systems excited by correlated stochastic processes
,” SIAM J. Uncertain. Quantif.
3
(1
), 709
–736
(2015
). 12.
S.
Kumarasamy
and A. N.
Pisarchik
, “Extreme events in systems with discontinuous boundaries
,” Phys. Rev. E
98
(3
), 032203
(2018
). 13.
B.
Thangavel
, S.
Srinivasan
, and T.
Kathamuthu
, “Extreme events in a forced BVP oscillator: Experimental and numerical studies
,” Chaos Soliton. Fract.
153
, 111569
(2021
). 14.
H. L. D. S.
Cavalcante
, M.
Oriá
, D.
Sornette
, E.
Ott
, and D. J.
Gauthier
, “Predictability and suppression of extreme events in a chaotic system
,” Phys. Rev. Lett.
111
(19
), 198701
(2013
). 15.
P.
Ashwin
, J.
Buescu
, and I.
Stewart
, “Bubbling of attractors and synchronisation of chaotic oscillators
,” Phys. Lett. A
193
(2
), 126
–139
(1994
). 16.
D.
Zhao
, Y.
Li
, Y.
Xu
, Q.
Liu
, and J.
Kurths
, “Extreme events in a class of nonlinear Duffing-type oscillators with a parametric periodic force
,” Eur. Phys. J. Plus
137
(3
), 314
(2022
). 17.
Q.
Liu
, Y.
Xu
, J.
Kurths
, and X.
Liu
, “Complex nonlinear dynamics and vibration suppression of conceptual airfoil models: A state-of-the-art overview
,” Chaos
32
(6
), 062101
(2022
). 18.
B.
Lindner
, J.
Garcıa-Ojalvo
, A.
Neiman
, and L.
Schimansky-Geier
, “Effects of noise in excitable systems
,” Phys. Rep.
392
(6
), 321
–424
(2004
). 19.
A. N.
Pisarchik
and U.
Feudel
, “Control of multistability
,” Phys. Rep.
540
(4
), 167
–218
(2014
). 20.
L.
Gammaitoni
, P.
Hänggi
, P.
Jung
, and F.
Marchesoni
, “Stochastic resonance
,” Rev. Mod. Phys.
70
(1
), 223
(1998
). 21.
H.
Li
, Y.
Xu
, R.
Metzler
, and J.
Kurths
, “Transition path properties for one-dimensional systems driven by Poisson white noise
,” Chaos Soliton. Fract.
141
, 110293
(2020
). 22.
Q.
Liu
, Y.
Xu
, and J.
Kurths
, “Bistability and stochastic jumps in an airfoil system with viscoelastic material property and random fluctuations
,” Commun. Nonlinear Sci. Numer. Simul.
84
, 105184
(2020
). 23.
C. L.
Franzke
, “Extremes in dynamic-stochastic systems
,” Chaos
27
(1
), 012101
(2017
). 24.
M. A.
Mohamad
and T. P.
Sapsis
, “Probabilistic response and rare events in Mathieu’s equation under correlated parametric excitation
,” Ocean Eng.
120
, 289
–297
(2016
). 25.
S.
Guth
and T. P.
Sapsis
, “Machine learning predictors of extreme events occurring in complex dynamical systems
,” Entropy
21
(10
), 925
(2019
). 26.
H.
Kyul Joo
, M. A.
Mohamad
, and T. P.
Sapsis
, “Heavy-tailed response of structural systems subjected to stochastic excitation containing extreme forcing events
,” J. Comput. Nonlinear Dyn.
13
(9
), 090914
(2018
). 27.
C.
Franzke
, “Predictability of extreme events in a nonlinear stochastic-dynamical model
,” Phys. Rev. E
85
(3
), 031134
(2012
). 28.
Q.
Liu
, Y.
Xu
, and Y.
Li
, “Complex dynamics of a conceptual airfoil structure with consideration of extreme flight conditions
,” Nonlinear Dyn.
(published online) (2023
). 29.
S.
Sudharsan
, A.
Venkatesan
, P.
Muruganandam
, and M.
Senthilvelan
, “Emergence and mitigation of extreme events in a parametrically driven system with velocity-dependent potential
,” Eur. Phys. J. Plus
136
(1
), 129
(2021
). 30.
J.
Zamora-Munt
, C. R.
Mirasso
, and R.
Toral
, “Suppression of deterministic and stochastic extreme desynchronization events using anticipated synchronization
,” Phys. Rev. E
89
(1
), 012921
(2014
). 31.
C.
Bonatto
and A.
Endler
, “Extreme and superextreme events in a loss-modulated CO
laser: Nonlinear resonance route and precursors
,” Phys. Rev. E
96
(1
), 012216
(2017
). 32.
A.
Jamnongpipatkul
, Z.
Su
, and J. M.
Falzarano
, “Nonlinear ship rolling motion subjected to noise excitation
,” Ocean Syst. Eng.
1
(3
), 249
–261
(2011
). 33.
J.
Chen
, J.
Yang
, K.
Shen
, Z.
Zheng
, and Z.
Chang
, “Stochastic dynamic analysis of rolling ship in random wave condition by using finite element method
,” Ocean Eng.
250
, 110973
(2022
). 34.
X.
Zhang
, Y.
Xu
, Q.
Liu
, J.
Kurths
, and C.
Grebogi
, “Rate-dependent tipping and early warning in a thermoacoustic system under extreme operating environment
,” Chaos
31
(11
), 113115
(2021
). 35.
F.
Yang
, Y.
Zheng
, J.
Duan
, L.
Fu
, and S.
Wiggins
, “The tipping times in an Arctic sea ice system under influence of extreme events
,” Chaos
30
(6
), 063125
(2020
). 36.
Z.
Wang
, Y.
Xu
, and H.
Yang
, “Lévy noise induced stochastic resonance in an FHN model
,” Sci. China Technol. Sci.
59
(3
), 371
–375
(2016
). 37.
X.
Yue
, B.
Yu
, Y.
Li
, and Y.
Xu
, “Dynamic response and bifurcation for Rayleigh-Liénard oscillator under multiplicative colored noise
,” Chaos Soliton. Fract.
155
, 111744
(2022
). 38.
X.
Yue
, G.
Lv
, and Y.
Zhang
, “Rare and hidden attractors in a periodically forced Duffing system with absolute nonlinearity
,” Chaos Soliton. Fract.
150
, 111108
(2021
). 39.
A.
Chudzik
, P.
Perlikowski
, A.
Stefanski
, and T.
Kapitaniak
, “Multistability and rare attractors in van der Pol–Duffing oscillator
,” Int. J. Bifurcation Chaos
21
(07
), 1907
–1912
(2011
). 40.
D.
Dudkowski
, S.
Jafari
, T.
Kapitaniak
, N. V.
Kuznetsov
, G. A.
Leonov
, and A.
Prasad
, “Hidden attractors in dynamical systems
,” Phys. Rep.
637
, 1
–50
(2016
). 41.
G.
Rega
and S.
Lenci
, “A global dynamics perspective for system safety from macro-to nanomechanics: Analysis, control, and design engineering
,” Appl. Mech. Rev.
67
(5
), 050802
(2015
). 42.
S.
Lenci
and G.
Rega
, Global Nonlinear Dynamics for Engineering Design and System Safety
(Springer
, 2019
), Vol. 588.43.
J.
Spiechowicz
, P.
Hänggi
, and J.
Łuczka
, “Brownian motors in the microscale domain: Enhancement of efficiency by noise
,” Phys. Rev. E
90
(3
), 032104
(2014
). 44.
Z.
Lin
, Y.
Liang
, J.
Zhao
, and J.
Li
, “Predicting solutions of the Lotka-Volterra equation using hybrid deep network
,” Theor. Appl. Mech. Lett.
12
(6
), 100384
(2022
). © 2023 Author(s). Published under an exclusive license by AIP Publishing.
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