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Moment equations for a spatially extended system of two competing species

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  • D. Valenti
  • L. Schimansky-Geier
  • X. Sailer
  • B. Spagnolo

Abstract

The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the dynamics of the two species. To describe the spatial distribution of the species we use a model based on Lotka-Volterra (LV) equations. By writing them in a mean field form, the corresponding moment equations for the species concentrations are obtained in Gaussian approximation. In this formalism the system dynamics is analyzed for different values of the multiplicative noise intensity. Finally by comparing these results with those obtained by direct simulations of the time discrete version of LV equations, that is coupled map lattice (CML) model, we conclude that the anticorrelated oscillations of the species densities are strictly related to non-overlapping spatial patterns. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Suggested Citation

  • D. Valenti & L. Schimansky-Geier & X. Sailer & B. Spagnolo, 2006. "Moment equations for a spatially extended system of two competing species," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 199-203, March.
    • Handle: RePEc:spr:eurphb:v:50:y:2006:i:1:p:199-203
    DOI: 10.1140/epjb/e2006-00102-5
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    1. Spagnolo, B. & Valenti, D. & Guarcello, C. & Carollo, A. & Persano Adorno, D. & Spezia, S. & Pizzolato, N. & Di Paola, B., 2015. "Noise-induced effects in nonlinear relaxation of condensed matter systems," Chaos, Solitons & Fractals, Elsevier, vol. 81(PB), pages 412-424.
    2. Dai, Shiqi & Lu, Lulu & Wei, Zhouchao & Zhu, Yuan & Yi, Ming, 2022. "Influence of temperature and noise on the propagation of subthreshold signal in feedforward neural network," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Jin, Yanfei & Wang, Haotian & Xu, Pengfei, 2023. "Noise-induced enhancement of stability and resonance in a tri-stable system with time-delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    4. Mansour, Mahmoud B.A. & Abobakr, Asmaa H., 2022. "Stochastic differential equation models for tumor population growth," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    5. Zhang, Wenyue & Shi, Peiming & Li, Mengdi & Han, Dongying, 2021. "A novel stochastic resonance model based on bistable stochastic pooling network and its application," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    6. Lumi, Neeme & Laas, Katrin & Mankin, Romi, 2015. "Rising relative fluctuation as a warning indicator of discontinuous transitions in symbiotic metapopulations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 109-118.
    7. Liu, Jian & Qiao, Zijian & Ding, Xiaojian & Hu, Bing & Zang, Chuanlai, 2021. "Stochastic resonance induced weak signal enhancement over controllable potential-well asymmetry," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    8. Zhao, Shengnan & Yuan, Sanling & Zhang, Tonghua, 2022. "The impact of environmental fluctuations on a plankton model with toxin-producing phytoplankton and patchy agglomeration," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    9. Xu, Pengfei & Jin, Yanfei, 2020. "Coherence and stochastic resonance in a second-order asymmetric tri-stable system with memory effects," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    10. Zhang, Qiumei & Jiang, Daqing, 2021. "Dynamics of stochastic predator-prey systems with continuous time delay," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    11. Zhang, Dongjian & Ma, Qihua & Dong, Hailiang & Liao, He & Liu, Xiangyu & Zha, Yibin & Zhang, Xiaoxiao & Qian, Xiaomin & Liu, Jin & Gan, Xuehui, 2023. "Time-delayed feedback bistable stochastic resonance system and its application in the estimation of the Polyester Filament Yarn tension in the spinning process," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    12. Fokou Kenfack, W. & Siewe Siewe, M. & Kofane, T.C., 2016. "Nonlinear dynamics and synchronization of saline oscillator’s model," Chaos, Solitons & Fractals, Elsevier, vol. 82(C), pages 72-82.
    13. Dong, Haitao & Shen, Xiaohong & He, Ke & Wang, Haiyan, 2020. "Nonlinear filtering effects of intrawell matched stochastic resonance with barrier constrainted duffing system for ship radiated line signature extraction," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    14. Mi, Li-Na & Guo, Yong-Feng & Zhang, Meng & Zhuo, Xiao-Jing, 2023. "Stochastic resonance in gene transcriptional regulatory system driven by Gaussian noise and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    15. Ren, Yuhao & Pan, Yan & Duan, Fabing, 2022. "SNR gain enhancement in a generalized matched filter using artificial optimal noise," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    16. Valenti, D. & Tranchina, L. & Brai, M. & Caruso, A. & Cosentino, C. & Spagnolo, B., 2008. "Environmental metal pollution considered as noise: Effects on the spatial distribution of benthic foraminifera in two coastal marine areas of Sicily (Southern Italy)," Ecological Modelling, Elsevier, vol. 213(3), pages 449-462.
    17. Tingting Zhang & Yanfei Jin, 2024. "Stochastic optimal control of a tri-stable energy harvester with the P-SSHI circuit under colored noise," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(1), pages 1-13, January.
    18. Li, Jiang-Cheng & Xu, Ming-Zhe & Han, Xu & Tao, Chen, 2022. "Dynamic risk resonance between crude oil and stock market by econophysics and machine learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    19. Xie, Tianting & Ji, Yuandong & Yang, Zhongshan & Duan, Fabing & Abbott, Derek, 2023. "Optimal added noise for minimizing distortion in quantizer-array linear estimation," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    20. Xu, Chaoqun, 2020. "Probabilistic mechanisms of the noise-induced oscillatory transitions in a Leslie type predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).

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