Noise in ecosystems: A short review

  • Received: 01 February 2004 Accepted: 29 June 2018 Published: 01 March 2004
  • MSC : 82Cxx,92D25.

  • Noise, through its interaction with the nonlinearity of the living systems, can give rise to counter-intuitive phenomena such as stochastic resonance, noise-delayed extinction, temporal oscillations, and spatial patterns. In this paper we briefly review the noise-induced effects in three different ecosystems: (i) two competing species; (ii) three interacting species, one predator and two preys, and (iii) N-interacting species. The transient dynamics of these ecosystems are analyzed through generalized Lotka-Volterra equations in the presence of multiplicative noise, which models the interaction between the species and the environment. The interaction parameter between the species is random in cases (i) and (iii), and a periodical function, which accounts for the environmental temperature, in case (ii). We find noise-induced phenomena such as quasi-deterministic oscillations, stochastic resonance, noise-delayed extinction, and noise-induced pattern formation with non-monotonic behaviors of patterns areas and of the density correlation as a function of the multiplicative noise intensity. The asymptotic behavior of the time average of theith population when the ecosystem is composed of a great number of interacting species is obtained and the effect of the noise on the asymptotic probability distri- butions of the populations is discussed.

    Citation: B. Spagnolo, D. Valenti, A. Fiasconaro. Noise in ecosystems: A short review[J]. Mathematical Biosciences and Engineering, 2004, 1(1): 185-211. doi: 10.3934/mbe.2004.1.185

    Related Papers:

    [1] Vadim S. Anishchenko, Tatjana E. Vadivasova, Galina I. Strelkova, George A. Okrokvertskhov . Statistical properties of dynamical chaos. Mathematical Biosciences and Engineering, 2004, 1(1): 161-184. doi: 10.3934/mbe.2004.1.161
    [2] Martin Baurmann, Wolfgang Ebenhöh, Ulrike Feudel . Turing instabilities and pattern formation in a benthic nutrient-microorganism system. Mathematical Biosciences and Engineering, 2004, 1(1): 111-130. doi: 10.3934/mbe.2004.1.111
    [3] Sangeeta Kumari, Sidharth Menon, Abhirami K . Dynamical system of quokka population depicting Fennecaphobia by Vulpes vulpes. Mathematical Biosciences and Engineering, 2025, 22(6): 1342-1363. doi: 10.3934/mbe.2025050
    [4] Raimund Bürger, Gerardo Chowell, Elvis Gavilán, Pep Mulet, Luis M. Villada . Numerical solution of a spatio-temporal predator-prey model with infected prey. Mathematical Biosciences and Engineering, 2019, 16(1): 438-473. doi: 10.3934/mbe.2019021
    [5] Glenn Webb, Martin J. Blaser, Huaiping Zhu, Sten Ardal, Jianhong Wu . Critical role of nosocomial transmission in the Toronto SARS outbreak. Mathematical Biosciences and Engineering, 2004, 1(1): 1-13. doi: 10.3934/mbe.2004.1.1
    [6] Sourav Kumar Sasmal, Jeet Banerjee, Yasuhiro Takeuchi . Dynamics and spatio-temporal patterns in a prey–predator system with aposematic prey. Mathematical Biosciences and Engineering, 2019, 16(5): 3864-3884. doi: 10.3934/mbe.2019191
    [7] Francesca Sapuppo, Elena Umana, Mattia Frasca, Manuela La Rosa, David Shannahoff-Khalsa, Luigi Fortuna, Maide Bucolo . Complex spatio-temporal features in meg data. Mathematical Biosciences and Engineering, 2006, 3(4): 697-716. doi: 10.3934/mbe.2006.3.697
    [8] Carolina Mendoza, Jean Bragard, Pier Luigi Ramazza, Javier Martínez-Mardones, Stefano Boccaletti . Pinning control of spatiotemporal chaos in the LCLV device. Mathematical Biosciences and Engineering, 2007, 4(3): 523-530. doi: 10.3934/mbe.2007.4.523
    [9] Ahmed Alshehri, Saif Ullah . A numerical study of COVID-19 epidemic model with vaccination and diffusion. Mathematical Biosciences and Engineering, 2023, 20(3): 4643-4672. doi: 10.3934/mbe.2023215
    [10] Raimund BÜrger, Gerardo Chowell, Elvis GavilÁn, Pep Mulet, Luis M. Villada . Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents. Mathematical Biosciences and Engineering, 2018, 15(1): 95-123. doi: 10.3934/mbe.2018004
  • Noise, through its interaction with the nonlinearity of the living systems, can give rise to counter-intuitive phenomena such as stochastic resonance, noise-delayed extinction, temporal oscillations, and spatial patterns. In this paper we briefly review the noise-induced effects in three different ecosystems: (i) two competing species; (ii) three interacting species, one predator and two preys, and (iii) N-interacting species. The transient dynamics of these ecosystems are analyzed through generalized Lotka-Volterra equations in the presence of multiplicative noise, which models the interaction between the species and the environment. The interaction parameter between the species is random in cases (i) and (iii), and a periodical function, which accounts for the environmental temperature, in case (ii). We find noise-induced phenomena such as quasi-deterministic oscillations, stochastic resonance, noise-delayed extinction, and noise-induced pattern formation with non-monotonic behaviors of patterns areas and of the density correlation as a function of the multiplicative noise intensity. The asymptotic behavior of the time average of theith population when the ecosystem is composed of a great number of interacting species is obtained and the effect of the noise on the asymptotic probability distri- butions of the populations is discussed.


  • This article has been cited by:

    1. S. L. Wang, X. L. Jin, Z. L. Huang, G. Q. Cai, Break-out of dynamic balance of nonlinear ecosystems using first passage failure theory, 2015, 80, 0924-090X, 1403, 10.1007/s11071-015-1951-2
    2. Partha Sarathi Mandal, Malay Banerjee, Stochastic persistence and stationary distribution in a Holling–Tanner type prey–predator model, 2012, 391, 03784371, 1216, 10.1016/j.physa.2011.10.019
    3. Yongfeng Guo, Yajun Shen, Jianguo Tan, Stochastic resonance in a piecewise nonlinear model driven by multiplicative non-Gaussian noise and additive white noise, 2016, 38, 10075704, 257, 10.1016/j.cnsns.2016.02.032
    4. Canrong Tian, Ling Lin, Lai Zhang, Additive noise driven phase transitions in a predator-prey system, 2017, 46, 0307904X, 423, 10.1016/j.apm.2017.01.087
    5. R.V. Bobryk, Stability analysis of a SIR epidemic model with random parametric perturbations, 2021, 143, 09600779, 110552, 10.1016/j.chaos.2020.110552
    6. N. Lumi, R. Mankin, 2015, 1685, 0094-243X, 050003, 10.1063/1.4934299
    7. Yu Zhao, Sanling Yuan, Tonghua Zhang, Stochastic periodic solution of a non-autonomous toxic-producing phytoplankton allelopathy model with environmental fluctuation, 2017, 44, 10075704, 266, 10.1016/j.cnsns.2016.08.013
    8. Changyou Wang, Linrui Li, Yuqian Zhou, Rui Li, On a delay ratio-dependent predator–prey system with feedback controls and shelter for the prey, 2018, 11, 1793-5245, 1850095, 10.1142/S179352451850095X
    9. Huiyan Zhao, Chongqi Zhang, Limin Wen, Maximum likelihood estimation for stochastic Lotka–Volterra model with jumps, 2018, 2018, 1687-1847, 10.1186/s13662-018-1605-z
    10. Hiroshi Serizawa, Takashi Amemiya, Kiminori Itoh, Sufficient noise and turbulence can induce phytoplankton patchiness, 2010, 02, 2150-4091, 320, 10.4236/ns.2010.24040
    11. D Valenti, G Denaro, F Conversano, C Brunet, A Bonanno, G Basilone, S Mazzola, B Spagnolo, The role of noise on the steady state distributions of phytoplankton populations, 2016, 2016, 1742-5468, 054044, 10.1088/1742-5468/2016/05/054044
    12. S. Spezia, L. Curcio, A. Fiasconaro, N. Pizzolato, D. Valenti, B. Spagnolo, P. Lo Bue, E. Peri, S. Colazza, Evidence of stochastic resonance in the mating behavior of Nezara viridula (L.), 2008, 65, 1434-6028, 453, 10.1140/epjb/e2008-00333-4
    13. Zheng-Lin Jia, Dong-Cheng Mei, Noise-induced phenomena in the dynamics of groundwater-dependent plant ecosystems with time delay, 2015, 2015, 1742-5468, P05034, 10.1088/1742-5468/2015/05/P05034
    14. D. Valenti, L. Schimansky-Geier, X. Sailer, B. Spagnolo, Moment equations for a spatially extended system of two competing species, 2006, 50, 1434-6028, 199, 10.1140/epjb/e2006-00102-5
    15. L. Ryashko, I. Bashkirtseva, A. Morozov, Stochastic Sensitivity Analysis and Control for Ecological Model with the Allee Effect, 2015, 10, 0973-5348, 130, 10.1051/mmnp/201510209
    16. Astero Provata, Igor M. Sokolov, Bernardo Spagnolo, Editorial: Ecological complex systems, 2008, 65, 1434-6028, 307, 10.1140/epjb/e2008-00380-9
    17. Chunhua Zeng, Qingshuang Xie, Tonghuan Wang, Chun Zhang, Xiaohui Dong, Lin Guan, Kongzhai Li, Weilong Duan, Stochastic ecological kinetics of regime shifts in a time‐delayed lake eutrophication ecosystem, 2017, 8, 2150-8925, 10.1002/ecs2.1805
    18. Kang-Kang Wang, Hui Ye, Ya-Jun Wang, Sheng-Hong Li, Time-delay-induced dynamical behaviors for an ecological vegetation growth system driven by cross-correlated multiplicative and additive noises, 2018, 41, 1292-8941, 10.1140/epje/i2018-11668-9
    19. Canrong Tian, Lai Zhang, Delay-driven irregular spatiotemporal patterns in a plankton system, 2013, 88, 1539-3755, 10.1103/PhysRevE.88.012713
    20. A. Fiasconaro, D. Valenti, B. Spagnolo, Asymptotic regime in N random interacting species, 2006, 50, 1434-6028, 189, 10.1140/epjb/e2006-00058-4
    21. D. Valenti, L. Tranchina, M. Brai, A. Caruso, C. Cosentino, B. Spagnolo, Environmental metal pollution considered as noise: Effects on the spatial distribution of benthic foraminifera in two coastal marine areas of Sicily (Southern Italy), 2008, 213, 03043800, 449, 10.1016/j.ecolmodel.2008.01.023
    22. 2009, 20095783, 978-1-4200-5214-5, 97, 10.1201/9781420052152.sec3
    23. Lutz Schimansky-Geier, Benjamin Lindner, Sebastian Milster, Alexander B. Neiman, Demixing of two species via reciprocally concentration-dependent diffusivity, 2021, 103, 2470-0045, 10.1103/PhysRevE.103.022113
    24. Dong-Wei Huang, Hong-Li Wang, Jian-Feng Feng, Zhi-Wen Zhu, Modelling algal densities in harmful algal blooms (HAB) with stochastic dynamics, 2008, 32, 0307904X, 1318, 10.1016/j.apm.2007.04.006
    25. Michael Assaf, Baruch Meerson, WKB theory of large deviations in stochastic populations, 2017, 50, 1751-8113, 263001, 10.1088/1751-8121/aa669a
    26. Yong-Feng Guo, Bei Xi, Fang Wei, Jian-Guo Tan, Stochastic resonance in FitzHugh–Nagumo neural system driven by correlated non-Gaussian noise and Gaussian noise, 2017, 31, 0217-9792, 1750264, 10.1142/S0217979217502642
    27. Stefania Scarsoglio, Paolo D’Odorico, Francesco Laio, Luca Ridolfi, Spatio-temporal stochastic resonance induces patterns in wetland vegetation dynamics, 2012, 10, 1476945X, 93, 10.1016/j.ecocom.2011.11.003
    28. Karen C. Abbott, Ben C. Nolting, Alternative (un)stable states in a stochastic predator–prey model, 2017, 32, 1476945X, 181, 10.1016/j.ecocom.2016.11.004
    29. Can Chen, Yanmei Kang, The asymptotic behavior of a stochastic vaccination model with backward bifurcation, 2016, 40, 0307904X, 6051, 10.1016/j.apm.2016.01.045
    30. Wenjie Cao, Tao Pan, DYNAMICS OF AN IMPULSIVE STOCHASTIC SIR EPIDEMIC MODEL WITH SATURATED INCIDENCE RATE, 2020, 10, 2156-907X, 1396, 10.11948/20190214
    31. An-Wei Li, Impact of noise on pattern formation in a predator–prey model, 2011, 66, 0924-090X, 689, 10.1007/s11071-010-9941-x
    32. Ranjit Kumar Upadhyay, Malay Banerjee, Rana Parshad, Sharada Nandan Raw, DETERMINISTIC CHAOS VERSUS STOCHASTIC OSCILLATION IN A PREY-PREDATOR-TOP PREDATOR MODEL, 2011, 16, 1392-6292, 343, 10.3846/13926292.2011.601767
    33. Evelyn Buckwar, Cónall Kelly, Asymptotic and Transient Mean-Square Properties of Stochastic Systems Arising in Ecology, Fluid Dynamics, and System Control, 2014, 74, 0036-1399, 411, 10.1137/120893859
    34. R. Mankin, T. Laas, E. Soika, A. Ainsaar, Noise-controlled slow–fast oscillations in predator–prey models with the Beddington functional response, 2007, 59, 1434-6028, 259, 10.1140/epjb/e2007-00285-1
    35. Alessandro Fiasconaro, Bernardo Spagnolo, Stability measures in metastable states with Gaussian colored noise, 2009, 80, 1539-3755, 10.1103/PhysRevE.80.041110
    36. Meng-Yu Tian, Can-Jun Wang, Ke-Li Yang, Peng Fu, Chun-Yan Xia, Xiao-Jing Zhuo, Lei Wang, Estimating the nonlinear effects of an ecological system driven by Ornstein-Uhlenbeck noise, 2020, 136, 09600779, 109788, 10.1016/j.chaos.2020.109788
    37. Wantao Jia, Yong Xu, Dongxi Li, Stochastic Dynamics of a Time-Delayed Ecosystem Driven by Poisson White Noise Excitation, 2018, 20, 1099-4300, 143, 10.3390/e20020143
    38. D. Valenti, G. Denaro, B. Spagnolo, S. Mazzola, G. Basilone, F. Conversano, C. Brunet, A. Bonanno, Stochastic models for phytoplankton dynamics in Mediterranean Sea, 2016, 27, 1476945X, 84, 10.1016/j.ecocom.2015.06.001
    39. Lev Ryashko, Stochastic Control in the Problem of Preventing Ecological Catastrophes, 2018, 51, 24058963, 540, 10.1016/j.ifacol.2018.11.478
    40. Irina Bashkirtseva, Lev Ryashko, Noise-induced shifts in the population model with a weak Allee effect, 2018, 491, 03784371, 28, 10.1016/j.physa.2017.08.157
    41. Irina Bashkirtseva, Lev Ryashko, Tatyana Ryazanova, Analysis of Noise-Induced Bifurcations in the Stochastic Tritrophic Population System, 2017, 27, 0218-1274, 1750208, 10.1142/S021812741750208X
    42. B. Spagnolo, S. Spezia, L. Curcio, N. Pizzolato, A. Fiasconaro, D. Valenti, P. Lo Bue, E. Peri, S. Colazza, Noise effects in two different biological systems, 2009, 69, 1434-6028, 133, 10.1140/epjb/e2009-00162-y
    43. Pintu Patra, Stefan Klumpp, Phenotypically heterogeneous populations in spatially heterogeneous environments, 2014, 89, 1539-3755, 10.1103/PhysRevE.89.030702
    44. Driss Kiouach, Lahcen Boulaasair, Stationary Distribution and Dynamic Behaviour of a Stochastic SIVR Epidemic Model with Imperfect Vaccine, 2018, 2018, 1110-757X, 1, 10.1155/2018/1291402
    45. Stefano Bonaccorsi, Stefania Ottaviano, Epidemics on networks with heterogeneous population and stochastic infection rates, 2016, 279, 00255564, 43, 10.1016/j.mbs.2016.07.002
    46. Irina Bashkirtseva, Darja Filippova, Alexander N. Pisarchik, 2016, 1790, 0094-243X, 150010, 10.1063/1.4968749
    47. P.S. Mandal, M. Banerjee, Multiplicative-noise Can Suppress Chaotic Oscillation in Lotka-Volterra Type Competitive Model, 2012, 7, 0973-5348, 23, 10.1051/mmnp/20127602
    48. Giuseppe Gaeta, Francesco Spadaro, Symmetry classification of scalar Ito equations with multiplicative noise, 2020, 27, 1776-0852, 679, 10.1080/14029251.2020.1819615
    49. Shengnan Zhao, Sanling Yuan, Hao Wang, Threshold behavior in a stochastic algal growth model with stoichiometric constraints and seasonal variation, 2020, 268, 00220396, 5113, 10.1016/j.jde.2019.11.004
    50. Changyou Wang, Yuqian Zhou, Yonghong Li, Rui Li, Well-posedness of a ratio-dependent Lotka–Volterra system with feedback control, 2018, 2018, 1687-2770, 10.1186/s13661-018-1039-2
    51. Alessandro Giuffrida, Davide Valenti, Graziella Ziino, Bernardo Spagnolo, Antonio Panebianco, A stochastic interspecific competition model to predict the behaviour of Listeria monocytogenes in the fermentation process of a traditional Sicilian salami, 2009, 228, 1438-2377, 767, 10.1007/s00217-008-0988-6
    52. Vicenç Méndez, S. I. Denisov, Daniel Campos, Werner Horsthemke, Role of the interpretation of stochastic calculus in systems with cross-correlated Gaussian white noises, 2014, 90, 1539-3755, 10.1103/PhysRevE.90.012116
    53. G. Bonanno, D. Valenti, B. Spagnolo, Role of noise in a market model with stochastic volatility, 2006, 53, 1434-6028, 405, 10.1140/epjb/e2006-00388-1
    54. V Schwämmle, S M D Queirós, E Brigatti, T Tchumatchenko, Competition and fragmentation: a simple model generating lognormal-like distributions, 2009, 11, 1367-2630, 093006, 10.1088/1367-2630/11/9/093006
    55. Werner Ebeling, Rainer Feistel, Susanne Feistel, On bifurcations in complex ecological systems with diffusion and noise, 2013, 14, 1476945X, 2, 10.1016/j.ecocom.2012.09.007
    56. Forest Harvesting Problem in the Light of the Information Measures, 2009, 4, 18193579, 25, 10.3923/tasr.2009.25.35
    57. Horst Malchow, Frank M. Hilker, Ivo Siekmann, Sergei V. Petrovskii, Alexander B. Medvinsky, 2008, Chapter 1, 978-3-7643-8590-3, 1, 10.1007/978-3-7643-8591-0_1
    58. Giuseppe Gaeta, Integration of the stochastic logistic equation via symmetry analysis, 2019, 26, 1402-9251, 454, 10.1080/14029251.2019.1613052
    59. Li Li, Zhi-Jun Wang, Dynamics in a predator–prey model with space and noise, 2013, 219, 00963003, 6542, 10.1016/j.amc.2013.01.002
    60. Irina Bashkirtseva, Lev Ryashko, Stochastic sensitivity analysis of noise-induced excitement in a prey–predator plankton system, 2011, 5, 2155-3769, 141, 10.1080/21553769.2012.702666
    61. Lei Zhang, Zhibin Li, Spatial Complexity of a Predator-Prey Model with Holling-Type Response, 2014, 2014, 1085-3375, 1, 10.1155/2014/675378
    62. Zhan-Wu Bai, Ping Wang, Escape rate of Brownian particles from a metastable potential well under time derivative Ornstein-Uhlenbeck noise, 2016, 89, 1434-6028, 10.1140/epjb/e2016-60940-x
    63. F. Müller, L. Schimansky-Geier, D.E. Postnov, Interaction of noise supported Ising–Bloch fronts with Dirichlet boundaries, 2013, 14, 1476945X, 21, 10.1016/j.ecocom.2012.11.002
    64. Neeme Lumi, Katrin Laas, Romi Mankin, Rising relative fluctuation as a warning indicator of discontinuous transitions in symbiotic metapopulations, 2015, 437, 03784371, 109, 10.1016/j.physa.2015.05.107
    65. Irina Bashkirtseva, Lev Ryashko, Analysis of the Noise-Induced Regimes in Ricker Population Model with Allee Effect via Confidence Domains Technique, 2014, 2014, 2314-6133, 1, 10.1155/2014/346239
    66. D. Valenti, A. Giuffrida, G. Denaro, N. Pizzolato, L. Curcio, S. Mazzola, G. Basilone, A. Bonanno, B. Spagnolo, A. Morozov, M. Ptashnyk, V. Volpert, Noise Induced Phenomena in the Dynamics of Two Competing Species, 2016, 11, 1760-6101, 158, 10.1051/mmnp/201611510
    67. M. Kodama, G. Hasegawa, M. Murata, 2009, Bandwidth-Based Congestion Control for TCP: Measurement Noise-Aware Parameter Settings and Self-Induced Oscillation, 978-1-4244-3437-4, 1, 10.1109/ICCW.2009.5207973
    68. R. Mbakob Yonkeu, R. Yamapi, G. Filatrella, C. Tchawoua, Stochastic bifurcations induced by correlated noise in a birhythmic van der Pol system, 2016, 33, 10075704, 70, 10.1016/j.cnsns.2015.09.005
    69. Anne Kjersti Bakken, Helge Bonesmo, Bård Pedersen, Spatial and Temporal Abundance of Interacting Populations of White Clover and Grass Species as Assessed by Image Analyses, 2015, 2015, 2314-8497, 1, 10.1155/2015/620164
    70. Dongwei Huang, Hongli Wang, Jianfeng Feng, Zhi-wen Zhu, Hopf bifurcation of the stochastic model on HAB nonlinear stochastic dynamics, 2006, 27, 09600779, 1072, 10.1016/j.chaos.2005.04.086
    71. Jiang-Cheng Li, Dong-Cheng Mei, Reverse resonance in stock prices of financial system with periodic information, 2013, 88, 1539-3755, 10.1103/PhysRevE.88.012811
    72. Qiao-Feng Lin, Can-Jun Wang, Ke-Li Yang, Meng-Yu Tian, Ya Wang, Jia-Liang Dai, Cross-correlated bounded noises induced the population extinction and enhancement of stability in a population growth model, 2019, 525, 03784371, 1046, 10.1016/j.physa.2019.04.020
    73. F. Borgogno, P. D'Odorico, F. Laio, L. Ridolfi, Mathematical models of vegetation pattern formation in ecohydrology, 2009, 47, 8755-1209, 10.1029/2007RG000256
    74. Giovanni Denaro, Davide Valenti, Bernardo Spagnolo, Gualtiero Basilone, Salvatore Mazzola, Salem W. Zgozi, Salvatore Aronica, Angelo Bonanno, Dante R. Chialvo, Dynamics of Two Picophytoplankton Groups in Mediterranean Sea: Analysis of the Deep Chlorophyll Maximum by a Stochastic Advection-Reaction-Diffusion Model, 2013, 8, 1932-6203, e66765, 10.1371/journal.pone.0066765
    75. Jose M. G. Vilar, J. Miguel Rubi, Determinants of population responses to environmental fluctuations, 2018, 8, 2045-2322, 10.1038/s41598-017-18976-6
    76. Davide Valenti, Bernardo Spagnolo, Stochastic dynamics and mean field approach in a system of three interacting species, 2009, 7, 2391-5471, 10.2478/s11534-009-0003-2
    77. O. A. Chichigina, Noise with memory as a model of lemming cycles, 2008, 65, 1434-6028, 347, 10.1140/epjb/e2008-00226-6
    78. Andrew Morozov, Giovanni Denaro, Bernardo Spagnolo, Davide Valenti, Revisiting the role of top-down and bottom-up controls in stabilisation of nutrient-rich plankton communities, 2019, 79, 10075704, 104885, 10.1016/j.cnsns.2019.104885
    79. Chunjin Wei, Yingjie Fu, Stationary Distribution and Periodic Solution of Stochastic Toxin-Producing Phytoplankton–Zooplankton Systems, 2020, 2020, 1076-2787, 1, 10.1155/2020/4627571
    80. S.P. Rajasekar, M. Pitchaimani, Qualitative analysis of stochastically perturbed SIRS epidemic model with two viruses, 2019, 118, 09600779, 207, 10.1016/j.chaos.2018.11.023
    81. Olga A Chichigina, Aleksey V Kargovsky, Davide Valenti, Role of sub- and super-Poisson noise sources in population dynamics, 2020, 2020, 1742-5468, 093501, 10.1088/1742-5468/abb369
    82. Gui-Quan Sun, Zhen Jin, Quan-Xing Liu, Bai-Lian Li, Rich dynamics in a predator–prey model with both noise and periodic force, 2010, 100, 03032647, 14, 10.1016/j.biosystems.2009.12.003
    83. A. La Cognata, D. Valenti, A. A. Dubkov, B. Spagnolo, Dynamics of two competing species in the presence of Lévy noise sources, 2010, 82, 1539-3755, 10.1103/PhysRevE.82.011121
    84. Changyou Wang, Nan Li, Yuqian Zhou, Xingcheng Pu, Rui Li, On a Multi-Delay Lotka-Volterra Predator-Prey Model with Feedback Controls and Prey Diffusion, 2019, 39, 0252-9602, 429, 10.1007/s10473-019-0209-3
    85. Olga A. Chichigina, Alexander A. Dubkov, Davide Valenti, Bernardo Spagnolo, Stability in a system subject to noise with regulated periodicity, 2011, 84, 1539-3755, 10.1103/PhysRevE.84.021134
    86. IRINA BASHKIRTSEVA, ANALYSIS OF LIMIT CYCLES RESPONSE ON PARAMETRIC NOISE IN ONE-DIMENSIONAL DISCRETE-TIME SYSTEMS, 2013, 12, 0219-4775, 1350009, 10.1142/S0219477513500090
    87. Yu Zhao, Sanling Yuan, Stability in distribution of a stochastic hybrid competitive Lotka–Volterra model with Lévy jumps, 2016, 85, 09600779, 98, 10.1016/j.chaos.2016.01.015
    88. Tapan Saha, M. Banerjee, Effect of small time delay in a predator-prey model within random environment, 2008, 16, 0971-3514, 225, 10.1007/s12591-008-0014-2
    89. R. Mbakob Yonkeu, R. Yamapi, G. Filatrella, C. Tchawoua, Pseudopotential of birhythmic van der Pol-type systems with correlated noise, 2016, 84, 0924-090X, 627, 10.1007/s11071-015-2512-4
    90. B. I. Camara, R. Yamapi, H Mokrani, Environmental stochastic effects on phytoplankton–zooplankton dynamics, 2019, 96, 0924-090X, 2013, 10.1007/s11071-019-04902-0
    91. Xiao-Chong Zhang, Gui-Quan Sun, Zhen Jin, Spatial dynamics in a predator-prey model with Beddington-DeAngelis functional response, 2012, 85, 1539-3755, 10.1103/PhysRevE.85.021924
    92. Davide Valenti, Giovanni Denaro, Bernardo Spagnolo, Fabio Conversano, Christophe Brunet, Francois G. Schmitt, How Diffusivity, Thermocline and Incident Light Intensity Modulate the Dynamics of Deep Chlorophyll Maximum in Tyrrhenian Sea, 2015, 10, 1932-6203, e0115468, 10.1371/journal.pone.0115468
    93. I. Bashkirtseva, L. Ryashko, Sensitivity analysis of stochastic attractors and noise-induced transitions for population model with Allee effect, 2011, 21, 1054-1500, 047514, 10.1063/1.3647316
    94. Quan-Xing Liu, Zhen Jin, Bai-Lian Li, Resonance and frequency-locking phenomena in spatially extended phytoplankton–zooplankton system with additive noise and periodic forces, 2008, 2008, 1742-5468, P05011, 10.1088/1742-5468/2008/05/P05011
    95. G. Denaro, D. Valenti, A. La Cognata, B. Spagnolo, A. Bonanno, G. Basilone, S. Mazzola, S.W. Zgozi, S. Aronica, C. Brunet, Spatio-temporal behaviour of the deep chlorophyll maximum in Mediterranean Sea: Development of a stochastic model for picophytoplankton dynamics, 2013, 13, 1476945X, 21, 10.1016/j.ecocom.2012.10.002
    96. Zheng-Lin Jia, Chun-Yan Yang, Chun Li, Dong-Cheng Mei, Stochastic resonance in a groundwater-dependent plant ecosystem with fluctuations and time delay, 2014, 2014, 1742-5468, P03022, 10.1088/1742-5468/2014/03/P03022
    97. Xiu-Deng Zheng, Cong Li, Sabin Lessard, Yi Tao, Evolutionary stability concepts in a stochastic environment, 2017, 96, 2470-0045, 10.1103/PhysRevE.96.032414
    98. Jiang-Cheng Li, Chun Li, Dong-Cheng Mei, Effects of time delay on stochastic resonance of the stock prices in financial system, 2014, 378, 03759601, 1997, 10.1016/j.physleta.2014.05.036
    99. Irina Bashkirtseva, Lev Ryashko, Tatyana Ryazanova, Stochastic variability and transitions to chaos in a hierarchical three-species population model, 2019, 119, 09600779, 276, 10.1016/j.chaos.2018.12.035
    100. Dianli Zhao, Sanling Yuan, Persistence and stability of the disease-free equilibrium in a stochastic epidemic model with imperfect vaccine, 2016, 2016, 1687-1847, 10.1186/s13662-016-1010-4
    101. Yuanlin Ma, Xingwang Yu, Threshold dynamics of a stochastic SIVS model with saturated incidence and Lévy jumps, 2020, 2020, 1687-1847, 10.1186/s13662-020-02723-9
    102. Elisabetta Tornatore, Pasquale Vetro, Stefania Maria Buccellato, SIVR epidemic model with stochastic perturbation, 2014, 24, 0941-0643, 309, 10.1007/s00521-012-1225-6
    103. Michael Sieber, Horst Malchow, Lutz Schimansky-Geier, Constructive effects of environmental noise in an excitable prey–predator plankton system with infected prey, 2007, 4, 1476945X, 223, 10.1016/j.ecocom.2007.06.005
    104. L. Ridolfi, C. Camporeale, P. D'Odorico, F. Laio, Transient growth induces unexpected deterministic spatial patterns in the Turing process, 2011, 95, 0295-5075, 18003, 10.1209/0295-5075/95/18003
    105. Hiroshi Serizawa, Takashi Amemiya, Kiminori Itoh, Noise-triggered regime shifts in a simple aquatic model, 2009, 6, 1476945X, 375, 10.1016/j.ecocom.2009.03.002
    106. D. T. Hristopulos, B. Spagnolo, D. Valenti, Open challenges in environmental data analysis and ecological complex systems (a) , 2020, 132, 0295-5075, 68001, 10.1209/0295-5075/132/68001
    107. Irina Bashkirtseva, Lev Ryashko, Noise-induced extinction in Bazykin-Berezovskaya population model, 2016, 89, 1434-6028, 10.1140/epjb/e2016-70345-6
    108. Giovanni Volpe, Jan Wehr, Dmitri Petrov, J Miguel Rubi, Thermal noise suppression: how much does it cost?, 2009, 42, 1751-8113, 095005, 10.1088/1751-8113/42/9/095005
    109. Tao Feng, Daniel Charbonneau, Zhipeng Qiu, Yun Kang, Dynamics of task allocation in social insect colonies: scaling effects of colony size versus work activities, 2021, 82, 0303-6812, 10.1007/s00285-021-01589-z
    110. Jinyu Wei, Bin Liu, Coexistence in a competition-diffusion-advection system with equal amount of total resources, 2021, 18, 1551-0018, 3543, 10.3934/mbe.2021178
    111. Paolo Lazzari, Roberto Grimaudo, Cosimo Solidoro, Davide Valenti, Stochastic 0-dimensional Biogeochemical Flux Model: Effect of temperature fluctuations on the dynamics of the biogeochemical properties in a marine ecosystem, 2021, 103, 10075704, 105994, 10.1016/j.cnsns.2021.105994
    112. Xueyong Zhou, Xiangyun Shi, Ming Wei, Dynamical behavior and optimal control of a stochastic mathematical model for cholera, 2022, 156, 09600779, 111854, 10.1016/j.chaos.2022.111854
    113. Manish Chaudhary, Mritunjay Kumar Singh, Anomalous transport for multispecies reactive system with first order decay: time-fractional model, 2022, 97, 0031-8949, 074001, 10.1088/1402-4896/ac71e0
    114. Anna Olivé Abelló, Beatriz Vinha, Francisco Machín, Francesco Zerbetto, Evangelos Bakalis, Eugenio Fraile-Nuez, Analysis of Volcanic Thermohaline Fluctuations of Tagoro Submarine Volcano (El Hierro Island, Canary Islands, Spain), 2021, 11, 2076-3263, 374, 10.3390/geosciences11090374
    115. Influence of periodic volatility on the stability of financial market, 2017, 66, 1000-3290, 040501, 10.7498/aps.66.040501
    116. Tian-Jiao Feng, Jie Mei, Rui-Wu Wang, Sabin Lessard, Yi Tao, Xiu-Deng Zheng, Noise-Induced Quasi-Heteroclinic Cycle in a Rock–Paper–Scissors Game with Random Payoffs, 2022, 12, 2153-0785, 1280, 10.1007/s13235-021-00414-y
    117. Marcelo A. Pires, Nuno Crokidakis, Sílvio M. Duarte Queirós, Randomness in ecology: The role of complexity on the Allee effect, 2022, 589, 03784371, 126548, 10.1016/j.physa.2021.126548
    118. Roberto Grimaudo, Paolo Lazzari, Cosimo Solidoro, Davide Valenti, Effects of solar irradiance noise on a complex marine trophic web, 2022, 12, 2045-2322, 10.1038/s41598-022-16236-w
    119. Peng Fu, Can-Jun Wang, Ke-Li Yang, Xu-Bo Li, Biao Yu, Reentrance-like vibrational resonance in a fractional-order birhythmic biological system, 2022, 155, 09600779, 111649, 10.1016/j.chaos.2021.111649
    120. Olga A. Chichigina, Davide Valenti, Strongly super-Poisson statistics replaced by a wide-pulse Poisson process: The billiard random generator, 2021, 153, 09600779, 111451, 10.1016/j.chaos.2021.111451
    121. Krishnendu Pal, Smita Deb, Partha Sharathi Dutta, Tipping points in spatial ecosystems driven by short-range correlated noise, 2022, 106, 2470-0045, 10.1103/PhysRevE.106.054412
    122. Daniel V. Olivença, Jacob D. Davis, Eberhard O. Voit, Inference of dynamic interaction networks: A comparison between Lotka-Volterra and multivariate autoregressive models, 2022, 2, 2673-7647, 10.3389/fbinf.2022.1021838
    123. Rodrigo Crespo-Miguel, Javier Jarillo, Francisco J Cao-García, Scaling of population resilience with dispersal length and habitat size, 2022, 2022, 1742-5468, 023501, 10.1088/1742-5468/ac4982
    124. Thibaut Arnoulx de Pirey, Leticia F. Cugliandolo, Vivien Lecomte, Frédéric van Wijland, Path integrals and stochastic calculus, 2023, 0001-8732, 1, 10.1080/00018732.2023.2199229
    125. Cong Li, Tianjiao Feng, Yi Tao, Xiudeng Zheng, Jiajia Wu, Weak selection and stochastic evolutionary stability in a stochastic replicator dynamics, 2023, 00225193, 111524, 10.1016/j.jtbi.2023.111524
    126. Andrew Yu. Morozov, Dalal Almutairi, Sergei V. Petrovskii, Ying-Cheng Lai, Long transients in discontinuous time-discrete models of population dynamics, 2023, 174, 09600779, 113707, 10.1016/j.chaos.2023.113707
    127. Fabio Bagarello, Phase transitions, KMS condition and decision making: an introductory model, 2023, 381, 1364-503X, 10.1098/rsta.2022.0377
    128. Andy Chia, Wai-Keong (Dariel) Mok, Changsuk Noh, Leong Chuan Kwek, Quantum pure noise-induced transitions: A truly nonclassical limit cycle sensitive to number parity, 2023, 15, 2542-4653, 10.21468/SciPostPhys.15.3.121
    129. Zeyan Yue, Sheng Wang, Dynamics of a stochastic hybrid delay food chain model with jumps in an impulsive polluted environment, 2023, 21, 1551-0018, 186, 10.3934/mbe.2024009
    130. Andrew Yu. Morozov, Dalal Almutairi, Sergei V. Petrovskii, Alan Hastings, Regime shifts, extinctions and long transients in models of population dynamics with density-dependent dispersal, 2024, 290, 00063207, 110419, 10.1016/j.biocon.2023.110419
    131. Chern Lee, Hai Ye, Hui Li, The physical mechanism of stochastic calculus in random walks, 2024, 2024, 1742-5468, 023207, 10.1088/1742-5468/ad1be1
    132. Koushik Garain, Partha Sarathi Mandal, Effects of Planktivorous Fish Community on a Two-Dimensional Plankton System with Allee Effect in Prey, 2024, 23, 1575-5460, 10.1007/s12346-024-01037-5
    133. Guido Occhipinti, Stefano Piani, Paolo Lazzari, Stochastic effects on plankton dynamics: Insights from a realistic 0-dimensional marine biogeochemical model, 2024, 15749541, 102778, 10.1016/j.ecoinf.2024.102778
    134. Guangyan Zhong, Jiang-Cheng Li, Multiple stochastic and inverse stochastic resonances with transition phenomena in complex corporate financial systems, 2024, 34, 1054-1500, 10.1063/5.0198165
    135. Swadesh Pal, Malay Banerjee, Roderick Melnik, Nonequilibrium dynamics in a noise-induced predator–prey model, 2025, 191, 09600779, 115884, 10.1016/j.chaos.2024.115884
    136. Chenfei Ma, Xiaofeng Zhang, Rong Yuan, Dynamic analysis of a stochastic regime-switching Lotka–Volterra competitive system with distributed delays and Ornstein–Uhlenbeck process, 2025, 190, 09600779, 115765, 10.1016/j.chaos.2024.115765
    137. Hui Zhang, Yi Tao, Cong Li, Impact of environmental stochastic fluctuations on the red-king effect in interspecific mutualism, 2025, 111, 2470-0045, 10.1103/PhysRevE.111.064201
    138. Mohsen Pourmohammad Shahvar, Davide Valenti, Alfonso Collura, Salvatore Micciche, Vittorio Farina, Giovanni Marsella, An Integrated Hybrid-Stochastic Framework for Agro-Meteorological Prediction Under Environmental Uncertainty, 2025, 8, 2571-905X, 30, 10.3390/stats8020030
  • Reader Comments
  • © 2004 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(5415) PDF downloads(1150) Cited by(137)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog