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Non-Gaussian noise-weakened stability in a foraging colony system with time delay

Author

Listed:
  • Dong, Xiaohui
  • Zeng, Chunhua
  • Yang, Fengzao
  • Guan, Lin
  • Xie, Qingshuang
  • Duan, Weilong

Abstract

In this paper, the dynamical properties in a foraging colony system with time delay and non-Gaussian noise were investigated. Using delay Fokker–Planck approach, the stationary probability distribution (SPD), the associated relaxation time (ART) and normalization correlation function (NCF) are obtained, respectively. The results show that: (i) the time delay and non-Gaussian noise can induce transition from a single peak to double peaks in the SPD, i.e., a type of bistability occurring in a foraging colony system where time delay and non-Gaussian noise not only cause transitions between stable states, but also construct the states themselves. Numerical simulations are presented and are in good agreement with the approximate theoretical results; (ii) there exists a maximum in the ART as a function of the noise intensity, this maximum for ART is identified as the characteristic of the non-Gaussian noise-weakened stability of the foraging colonies in the steady state; (iii) the ART as a function of the noise correlation time exhibits a maximum and a minimum, where the minimum for ART is identified as the signature of the non-Gaussian noise-enhanced stability of the foraging colonies; and (iv) the time delay can enhance the stability of the foraging colonies in the steady state, while the departure from Gaussian noise can weaken it, namely, the time delay and departure from Gaussian noise play opposite roles in ART or NCF.

Suggested Citation

  • Dong, Xiaohui & Zeng, Chunhua & Yang, Fengzao & Guan, Lin & Xie, Qingshuang & Duan, Weilong, 2018. "Non-Gaussian noise-weakened stability in a foraging colony system with time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 851-870.
    • Handle: RePEc:eee:phsmap:v:492:y:2018:i:c:p:851-870
    DOI: 10.1016/j.physa.2017.11.015
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    Citations

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    Cited by:

    1. Wu, Jian-Li & Duan, Wei-Long & Luo, Yuhui & Yang, Fengzao, 2020. "Time delay and non-Gaussian noise-enhanced stability of foraging colony system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    2. Cheng, Guanghui & Gui, Rong & Yao, Yuangen & Yi, Ming, 2019. "Enhancement of temporal regularity and degradation of spatial synchronization induced by cross-correlated sine-Wiener noises in regular and small-world neuronal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 361-369.
    3. Zhong, Guang-Yan & Li, Jiang-Cheng & Jiang, George J. & Li, Hai-Feng & Tao, Hui-Ming, 2018. "The time delay restraining the herd behavior with Bayesian approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 335-346.
    4. Bhowal, Sanchayan & Samanta, Ramkrishna Jyoti & Ray, Arnob & Bhattacharyya, Sirshendu & Hens, Chittaranjan, 2023. "Exploring the potential of collective learning to reduce foraging time," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    5. Dong, Yang & Wen, Shu-hui & Hu, Xiao-bing & Li, Jiang-Cheng, 2020. "Stochastic resonance of drawdown risk in energy market prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    6. Zhang, Hongxia & Xu, Wei & Guo, Qin & Han, Ping & Qiao, Yan, 2020. "First escape probability and mean first exit time for a time-delayed ecosystem driven by non-Gaussian colored noise," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    7. Tao, Chen & Zhong, Guang-Yan & Li, Jiang-Cheng, 2023. "Dynamic correlation and risk resonance among industries of Chinese stock market: New evidence from time–frequency domain and complex network perspectives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 614(C).
    8. Duan, Wei-Long & Fang, Hui, 2020. "The unified colored noise approximation of multidimensional stochastic dynamic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    9. Guo, Di & Li, Chun & Mei, Dong-Cheng, 2019. "Switch process induced by the sine-Wiener noises in the gene transcriptional regulatory system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1192-1202.

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