IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v153y2021ip1s0960077921008055.html
   My bibliography  Save this article

Strongly super-Poisson statistics replaced by a wide-pulse Poisson process: The billiard random generator

Author

Listed:
  • Chichigina, Olga A.
  • Valenti, Davide

Abstract

In this paper we present a study on random processes consisting of delta pulses characterized by strongly super-Poisson statistics and calculate its spectral density. We suggest a method for replacing a strongly super-Poisson process with a wide-pulse Poisson process, while demonstrating that these two processes can be set in such a way to have similar spectral densities, the same mean values, and the same correlation times. We also present a billiard system that can be used to generate random pulse noise of arbitrary statistical properties. The particle dynamics is considered in terms of delta and wide pulses simultaneously. The results of numerical experiments with the billiard system are in a good agreement with the analytical findings.

Suggested Citation

  • Chichigina, Olga A. & Valenti, Davide, 2021. "Strongly super-Poisson statistics replaced by a wide-pulse Poisson process: The billiard random generator," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p1:s0960077921008055
    DOI: 10.1016/j.chaos.2021.111451
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921008055
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111451?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. William J. Blake & Mads KÆrn & Charles R. Cantor & J. J. Collins, 2003. "Noise in eukaryotic gene expression," Nature, Nature, vol. 422(6932), pages 633-637, April.
    2. O. Chichigina, 2008. "Noise with memory as a model of lemming cycles," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(3), pages 347-352, October.
    3. Mátyás, L. & Barna, I.F., 2011. "Geometrical origin of chaoticity in the bouncing ball billiard," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1111-1116.
    4. Pease, April & Mahmoodi, Korosh & West, Bruce J., 2018. "Complexity measures of music," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 82-86.
    5. Zhang, Xiaolei & Ma, Renjun & Wang, Lin, 2020. "Predicting turning point, duration and attack rate of COVID-19 outbreaks in major Western countries," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    6. Sokolov, I.M. & Belik, V.V., 2003. "Competition between Lévy jumps and continuous drift," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(1), pages 46-52.
    7. Ward Whitt, 1982. "Approximating a Point Process by a Renewal Process, I: Two Basic Methods," Operations Research, INFORMS, vol. 30(1), pages 125-147, February.
    8. P. Turchin & L. Oksanen & P. Ekerholm & T. Oksanen & H. Henttonen, 2000. "Are lemmings prey or predators?," Nature, Nature, vol. 405(6786), pages 562-565, June.
    9. Allegrini, P. & Barbi, F. & Grigolini, P. & Paradisi, P., 2007. "Aging and renewal events in sporadically modulated systems," Chaos, Solitons & Fractals, Elsevier, vol. 34(1), pages 11-18.
    10. Astero Provata & Igor Sokolov & Bernardo Spagnolo, 2008. "Editorial: Ecological complex systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(3), pages 307-314, October.
    11. Iliopoulos, A. & Chorozoglou, D. & Kourouklas, C. & Mangira, O. & Papadimitriou, E., 2020. "Memory and renewal aging of strong earthquakes in Hellenic seismicity," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Hongying & Yao, Chengli, 2017. "The influence of internal noise on the detection of hormonal signal with the existence of external noise in a cell system," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 1-6.
    2. Mohammad Soltani & Cesar A Vargas-Garcia & Duarte Antunes & Abhyudai Singh, 2016. "Intercellular Variability in Protein Levels from Stochastic Expression and Noisy Cell Cycle Processes," PLOS Computational Biology, Public Library of Science, vol. 12(8), pages 1-23, August.
    3. Dong, Jinlu & Fang, Jianhong & Pan, Jingwu & Hong, Guangyang & Li, Jian, 2022. "Dynamic model of vibrating plate coupled with a granule bed," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    4. Ramirez-Aristizabal, Adolfo G. & Médé, Butovens & Kello, Christopher T., 2018. "Complexity matching in speech: Effects of speaking rate and naturalness," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 175-179.
    5. Zahra Dehghan Shabani & Rouhollah Shahnazi, 2020. "Spatial distribution dynamics and prediction of COVID‐19 in Asian countries: spatial Markov chain approach," Regional Science Policy & Practice, Wiley Blackwell, vol. 12(6), pages 1005-1025, December.
    6. Singhal, Amit & Singh, Pushpendra & Lall, Brejesh & Joshi, Shiv Dutt, 2020. "Modeling and prediction of COVID-19 pandemic using Gaussian mixture model," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    7. Chih-Yuan Hsu & Bor-Sen Chen, 2016. "Systematic Design of a Metal Ion Biosensor: A Multi-Objective Optimization Approach," PLOS ONE, Public Library of Science, vol. 11(11), pages 1-16, November.
    8. Pradhan, Salil & Damodaran, Purushothaman & Srihari, Krishnaswami, 2008. "Predicting performance measures for Markovian type of manufacturing systems with product failures," European Journal of Operational Research, Elsevier, vol. 184(2), pages 725-744, January.
    9. Girish, Muckai K. & Hu, Jian-Qiang, 2000. "Higher order approximations for the single server queue with splitting, merging and feedback," European Journal of Operational Research, Elsevier, vol. 124(3), pages 447-467, August.
    10. Masselink, Inge H.J. & van der Mijden, Thomas L.C. & Litvak, Nelly & Vanberkel, Peter T., 2012. "Preparation of chemotherapy drugs: Planning policy for reduced waiting times," Omega, Elsevier, vol. 40(2), pages 181-187, April.
    11. Zhou, Xueyong & Shi, Xiangyun & Wei, Ming, 2022. "Dynamical behavior and optimal control of a stochastic mathematical model for cholera," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    12. Luca Bonacini & Giovanni Gallo & Fabrizio Patriarca, 2021. "Identifying policy challenges of COVID-19 in hardly reliable data and judging the success of lockdown measures," Journal of Population Economics, Springer;European Society for Population Economics, vol. 34(1), pages 275-301, January.
    13. Berkley, Blair J., 1996. "Analyzing service blueprints using phase distributions," European Journal of Operational Research, Elsevier, vol. 88(1), pages 152-164, January.
    14. Shin, Yang Woo & Moon, Dug Hee, 2011. "Approximation of M/M/c retrial queue with PH-retrial times," European Journal of Operational Research, Elsevier, vol. 213(1), pages 205-209, August.
    15. Blasi, Monica Francesca & Casorelli, Ida & Colosimo, Alfredo & Blasi, Francesco Simone & Bignami, Margherita & Giuliani, Alessandro, 2005. "A recursive network approach can identify constitutive regulatory circuits in gene expression data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 349-370.
    16. Amaral, Marco A. & Oliveira, Marcelo M. de & Javarone, Marco A., 2021. "An epidemiological model with voluntary quarantine strategies governed by evolutionary game dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    17. Chunjuan Zhu & Zibo Chen & Qiwen Sun, 2022. "Stochastic Transcription with Alterable Synthesis Rates," Mathematics, MDPI, vol. 10(13), pages 1-20, June.
    18. Swapnarekha, H. & Behera, Himansu Sekhar & Nayak, Janmenjoy & Naik, Bighnaraj, 2020. "Role of intelligent computing in COVID-19 prognosis: A state-of-the-art review," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    19. Huang, Chiou-Jye & Shen, Yamin & Kuo, Ping-Huan & Chen, Yung-Hsiang, 2022. "Novel spatiotemporal feature extraction parallel deep neural network for forecasting confirmed cases of coronavirus disease 2019," Socio-Economic Planning Sciences, Elsevier, vol. 80(C).
    20. Vladislav Soukhovolsky & Anton Kovalev & Yulia Ivanova & Olga Tarasova, 2023. "Autoregression, First Order Phase Transition, and Stochastic Resonance: A Comparison of Three Models for Forest Insect Outbreaks," Mathematics, MDPI, vol. 11(19), pages 1-19, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:153:y:2021:i:p1:s0960077921008055. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.