https://doi.org/10.1140/epjp/s13360-025-06617-1
Regular Article
Nonlinear dynamical analysis of a fractional-order El Niño Southern Oscillation system
1
Mathematical and Computational Sciences (Physical Sciences Division), IASST, 781035, Guwahati, India
2
Department of Mathematics, Girijananda Chowdhury University, 781017, Guwahati, India
3
Department of Mathematics, Gauhati University, 781014, Guwahati, India
4
Academy of Scientific and Innovative Research (AcSIR), 201002, Ghaziabad, India
5
Center for Wildlife and Environmental Studies, Girijananda Chowdhury University, Guwahati, India
a
ajkashyap.maths@gmail.com
b
d.santu@iasst.gov.in
Received:
22
April
2025
Accepted:
3
July
2025
Published online:
28
July
2025
Advancements in climate modeling have played a vital role in reducing the adverse effects of climate-related disasters. Among the key drivers of global climatic variability is the El Niño–Southern Oscillation (ENSO), a naturally recurring phenomenon marked by periodic warming and cooling of the central and eastern tropical Pacific Ocean. In this study, we investigate a coupled oscillator model of ENSO within the framework of Caputo-type fractional derivatives, offering a generalized approach to capturing memory effects and hereditary properties inherent in climate systems. We provide rigorous theoretical analysis, including the existence, uniqueness, and stability of solutions, and identify Pitchfork and Hopf bifurcations marking critical transitions. Extensive numerical simulations demonstrate the model’s sensitivity to fractional order and other parameters, revealing complex dynamics such as Bogdanov–Takens and period-doubling bifurcations. Notably, a catastrophic bifurcation emerges at a critical fractional order, where the system transitions from stable equilibrium to limit cycle oscillations. This underscores the importance of memory effects in ENSO dynamics and offers a realistic framework for understanding abrupt shifts and sustained oscillatory behavior in the climate system.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
