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Rai A, Nath Sharma B, Rabindrajit Luwang S, Nurujjaman M, Majhi S. Identifying extreme events in the stock market: A topological data analysis. CHAOS (WOODBURY, N.Y.) 2024; 34:103106. [PMID: 39352199 DOI: 10.1063/5.0220424] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2024] [Accepted: 09/09/2024] [Indexed: 10/03/2024]
Abstract
This paper employs Topological Data Analysis (TDA) to detect extreme events (EEs) in the stock market at a continental level. Previous approaches, which analyzed stock indices separately, could not detect EEs for multiple time series in one go. TDA provides a robust framework for such analysis and identifies the EEs during the crashes for different indices. The TDA analysis shows that L1, L2 norms and Wasserstein distance (WD) of the world leading indices rise abruptly during the crashes, surpassing a threshold of μ+4∗σ, where μ and σ are the mean and the standard deviation of norm or WD, respectively. Our study identified the stock index crashes of the 2008 financial crisis and the COVID-19 pandemic across continents as EEs. Given that different sectors in an index behave differently, a sector-wise analysis was conducted during the COVID-19 pandemic for the Indian stock market. The sector-wise results show that after the occurrence of EE, we have observed strong crashes surpassing μ+2∗σ for an extended period for the banking, automobile, IT, realty, energy, and metal sectors. While for the pharmaceutical and FMCG sectors, no significant spikes were noted. Hence, TDA also proves successful in identifying the duration of shocks after the occurrence of EEs. This also indicates that the banking sector continued to face stress and remained volatile even after the crash. This study gives us the applicability of TDA as a powerful analytical tool to study EEs in various fields.
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Affiliation(s)
- Anish Rai
- Department of Physics, National Institute of Technology Sikkim, Ravangla, Sikkim 737139, India
| | - Buddha Nath Sharma
- Department of Physics, National Institute of Technology Sikkim, Ravangla, Sikkim 737139, India
| | | | - Md Nurujjaman
- Department of Physics, National Institute of Technology Sikkim, Ravangla, Sikkim 737139, India
| | - Sushovan Majhi
- Data Science Program, George Washington University, Washington, DC 20052, USA
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Kumarasamy S, Leo Kingston S, Srinivasan S, Chudzik A, Kathamuthu T, Kapitaniak T. Extreme events and extreme multistability in a nearly conservative system. CHAOS (WOODBURY, N.Y.) 2024; 34:071103. [PMID: 39052925 DOI: 10.1063/5.0223470] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2024] [Accepted: 07/02/2024] [Indexed: 07/27/2024]
Abstract
This study investigates the emergence of extreme events in a complex variable dynamical system. In the absence of an external forcing, the model exhibits nearly Hamiltonian dynamics. When we set the system to a nearly conservative state and perturb it with external forcing, the formation of the onset of the extreme events was detected. By applying nullcline analysis and the system's vector field, we explored the underlying mechanism that leads to extreme events. Furthermore, we have conducted a thorough investigation to show the dynamic origins of extreme amplitude events and their transitions. The hardware electronic experiment is used to validate the numerical results of the onset of extreme events, and the results obtained are in good agreement with one another.
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Affiliation(s)
- Suresh Kumarasamy
- Centre for Computational Modeling, Chennai Institute of Technology, Chennai 600069, Tamil Nadu, India
| | - S Leo Kingston
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Sabarathinam Srinivasan
- Centre for Computational Modeling, Chennai Institute of Technology, Chennai 600069, Tamil Nadu, India
| | - Agnieszka Chudzik
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Thamilmaran Kathamuthu
- Centre for Computational Modeling, Chennai Institute of Technology, Chennai 600069, Tamil Nadu, India
| | - Tomasz Kapitaniak
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
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Leo Kingston S, Kumaran G, Ghosh A, Kumarasamy S, Kapitaniak T. Impact of time varying interaction: Formation and annihilation of extreme events in dynamical systems. CHAOS (WOODBURY, N.Y.) 2023; 33:123134. [PMID: 38154041 DOI: 10.1063/5.0174366] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2023] [Accepted: 11/30/2023] [Indexed: 12/30/2023]
Abstract
This study investigates the emergence of extreme events in two different coupled systems: the FitzHugh-Nagumo neuron model and the forced Liénard system, both based on time-varying interactions. The time-varying coupling function between the systems determines the duration and frequency of their interaction. Extreme events in the coupled system arise as a result of the influence of time-varying interactions within various parameter regions. We specifically focus on elucidating how the transition point between extreme events and regular events shifts in response to the duration of interaction time between the systems. By selecting the appropriate interaction time, we can effectively mitigate extreme events, which is highly advantageous for controlling undesired fluctuations in engineering applications. Furthermore, we extend our investigation to networks of oscillators, where the interactions among network elements are also time dependent. The proposed approach for coupled systems holds wide applicability to oscillator networks.
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Affiliation(s)
- S Leo Kingston
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Gayathri Kumaran
- Department of Electronics and Communication Engineering, Chennai Institute of Technology, Chennai 600069, Tamil Nadu, India
| | - Anupam Ghosh
- Department of Complex Systems, Institute of Computer Science, Czech Academy of Sciences, Prague 18207, Czech Republic
| | - Suresh Kumarasamy
- Centre for Computational Modeling, Chennai Institute of Technology, Chennai 600069, Tamil Nadu, India
| | - Tomasz Kapitaniak
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
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Mishra A, Saha S, Ghosh S, Dana SK, Hens C. Contrarian role of phase and phase velocity coupling in synchrony of second-order phase oscillators. Phys Rev E 2023; 108:L042201. [PMID: 37978600 DOI: 10.1103/physreve.108.l042201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2023] [Accepted: 10/02/2023] [Indexed: 11/19/2023]
Abstract
Positive phase coupling plays an attractive role in inducing in-phase synchrony in an ensemble of phase oscillators. Positive coupling involving both amplitude and phase continues to be attractive, leading to complete synchrony in identical oscillators (limit cycle or chaotic) or phase coherence in oscillators with heterogeneity of parameters. In contrast, purely positive phase velocity coupling may originate a repulsive effect on pendulumlike oscillators (with rotational motion) to bring them into a state of diametrically opposite phases or a splay state. Negative phase velocity coupling is necessary to induce synchrony or coherence in the general sense. The contrarian roles of phase coupling and phase velocity coupling on the synchrony of networks of second-order phase oscillators have been explored here. We explain our proposition using networks of two model systems, a second-order phase oscillator representing the pendulum or the superconducting Josephson junction dynamics, and a voltage-controlled oscillations in neurons model. Numerical as well as semianalytical approaches are used to confirm our results.
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Affiliation(s)
- Arindam Mishra
- Department of Physics, National University of Singapore, Singapore 117551, Singapore
| | - Suman Saha
- National Brain Research Centre, Manesar, Gurugram 122051, India
| | - Subrata Ghosh
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Gachibowli, Hyderabad 500 032, India
| | - Syamal Kumar Dana
- Department of Mathematics, Jadavpur University, Kolkata 700032, India
- Division of Dynamics, Lodz University of Technology, 90-924 Lodz, Poland
| | - Chittaranjan Hens
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Gachibowli, Hyderabad 500 032, India
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Mishra A, Saha S, Dana SK. Chimeras in globally coupled oscillators: A review. CHAOS (WOODBURY, N.Y.) 2023; 33:092101. [PMID: 37703474 DOI: 10.1063/5.0143872] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2023] [Accepted: 08/21/2023] [Indexed: 09/15/2023]
Abstract
The surprising phenomenon of chimera in an ensemble of identical oscillators is no more strange behavior of network dynamics and reality. By this time, this symmetry breaking self-organized collective dynamics has been established in many networks, a ring of non-locally coupled oscillators, globally coupled networks, a three-dimensional network, and multi-layer networks. A variety of coupling and dynamical models in addition to the phase oscillators has been used for a successful observation of chimera patterns. Experimental verification has also been done using metronomes, pendula, chemical, and opto-electronic systems. The phenomenon has also been shown to appear in small networks, and hence, it is not size-dependent. We present here a brief review of the origin of chimera patterns restricting our discussions to networks of globally coupled identical oscillators only. The history of chimeras in globally coupled oscillators is older than what has been reported in nonlocally coupled phase oscillators much later. We elaborate the story of the origin of chimeras in globally coupled oscillators in a chronological order, within our limitations, and with brief descriptions of the significant contributions, including our personal experiences. We first introduce chimeras in non-locally coupled and other network configurations, in general, and then discuss about globally coupled networks in more detail.
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Affiliation(s)
- Arindam Mishra
- Department of Physics, National University of Singapore, Singapore 117551
| | - Suman Saha
- Cognitive Brain Dynamics Laboratory, National Brain Research Centre, Gurugram 122051, India
| | - Syamal K Dana
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
- Division of Dynamics, Lodz University of Technology, 90-924 Lodz, Poland
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Pal TK, Ray A, Nag Chowdhury S, Ghosh D. Extreme rotational events in a forced-damped nonlinear pendulum. CHAOS (WOODBURY, N.Y.) 2023; 33:2895983. [PMID: 37307164 DOI: 10.1063/5.0152699] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Accepted: 05/11/2023] [Indexed: 06/14/2023]
Abstract
Since Galileo's time, the pendulum has evolved into one of the most exciting physical objects in mathematical modeling due to its vast range of applications for studying various oscillatory dynamics, including bifurcations and chaos, under various interests. This well-deserved focus aids in comprehending various oscillatory physical phenomena that can be reduced to the equations of the pendulum. The present article focuses on the rotational dynamics of the two-dimensional forced-damped pendulum under the influence of the ac and dc torque. Interestingly, we are able to detect a range of the pendulum's length for which the angular velocity exhibits a few intermittent extreme rotational events that deviate significantly from a certain well-defined threshold. The statistics of the return intervals between these extreme rotational events are supported by our data to be spread exponentially at a specific pendulum's length beyond which the external dc and ac torque are no longer sufficient for a full rotation around the pivot. The numerical results show a sudden increase in the size of the chaotic attractor due to interior crisis, which is the source of instability that is responsible for triggering large amplitude events in our system. We also notice the occurrence of phase slips with the appearance of extreme rotational events when the phase difference between the instantaneous phase of the system and the externally applied ac torque is observed.
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Affiliation(s)
- Tapas Kumar Pal
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Arnob Ray
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Sayantan Nag Chowdhury
- Department of Environmental Science and Policy, University of California, Davis, California 95616, USA
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
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