Many dynamical systems exhibit unexpected large amplitude excursions in the chronological progression of a state variable. In the present work, we consider the dynamics associated with the one-dimensional Higgs oscillator, which is realized through gnomonic projection of a harmonic oscillator defined on a spherical space of constant curvature onto a Euclidean plane, which is tangent to the spherical space. While studying the dynamics of such a Higgs oscillator subjected to damping and an external forcing, various bifurcation phenomena, such as symmetry breaking, period doubling, and intermittency crises are encountered. As the driven parameter increases, the route to chaos takes place via intermittency crisis, and we also identify the occurrence of extreme events due to the interior crisis. The study of probability distribution also confirms the occurrence of extreme events. Finally, we train the long short-term memory neural network model with the time-series data to forecast extreme events.
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February 2025
Research Article|
February 03 2025
Extreme events in the Higgs oscillator: A dynamical study and forecasting approach
Wasif Ahamed M
;
Wasif Ahamed M
a)
(Conceptualization, Formal analysis, Methodology, Software, Writing – original draft)
1
PG & Research Department of Physics, Nehru Memorial College (Autonomous), Affiliated to Bharathidasan University
, Puthanampatti, Tiruchirappalli 621 007, India
2
Department of Nonlinear Dynamics, School of Physics, Bharathidasan University
, Tiruchirappalli 620 024, India
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Kavitha R;
Kavitha R
b)
(Conceptualization, Formal analysis, Writing – original draft)
1
PG & Research Department of Physics, Nehru Memorial College (Autonomous), Affiliated to Bharathidasan University
, Puthanampatti, Tiruchirappalli 621 007, India
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Chithiika Ruby V
;
Chithiika Ruby V
c)
(Conceptualization, Formal analysis, Methodology, Supervision, Writing – original draft)
3
Center for Nonlinear and Complex Networks, SRM TRP Engineering College
, Tiruchirappalli, Tamil Nadu 621 105, India
4
Center for Research, Easwari Engineering College
, Chennai, Tamil Nadu 600 089, India
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Sathish Aravindh M
;
Sathish Aravindh M
d)
(Conceptualization, Formal analysis, Methodology, Software, Supervision, Writing – original draft)
2
Department of Nonlinear Dynamics, School of Physics, Bharathidasan University
, Tiruchirappalli 620 024, India
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Venkatesan A
;
Venkatesan A
e)
(Conceptualization, Investigation, Methodology, Supervision, Validation, Writing – review & editing)
1
PG & Research Department of Physics, Nehru Memorial College (Autonomous), Affiliated to Bharathidasan University
, Puthanampatti, Tiruchirappalli 621 007, India
e)Author to whom correspondence should be addressed: [email protected]
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Lakshmanan M
Lakshmanan M
f)
(Funding acquisition, Methodology, Supervision, Validation, Writing – review & editing)
2
Department of Nonlinear Dynamics, School of Physics, Bharathidasan University
, Tiruchirappalli 620 024, India
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e)Author to whom correspondence should be addressed: [email protected]
a)
Electronic mail: [email protected]
b)
Electronic mail: [email protected]
c)
Electronic mail: [email protected]
d)
Electronic mail: [email protected]
f)
Electronic mail: [email protected]
Chaos 35, 023119 (2025)
Article history
Received:
November 11 2024
Accepted:
January 13 2025
Citation
Wasif Ahamed M, Kavitha R, Chithiika Ruby V, Sathish Aravindh M, Venkatesan A, Lakshmanan M; Extreme events in the Higgs oscillator: A dynamical study and forecasting approach. Chaos 1 February 2025; 35 (2): 023119. https://doi.org/10.1063/5.0248180
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