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Complex spatiotemporal dynamics in an eco-epidemic model: Turing instability, non-stationary patterns, and chaos control

Author

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  • Majee, Suvankar
  • Jana, Soovoojeet
  • R., Anand
  • Ramprabhakar, J.

Abstract

This study presents the formulation of a spatiotemporal eco-epidemic model that takes into account an infectious disease affecting the prey population incorporating prey refugees and intraspecific competition of predators. In this work, we mainly focus on the interior equilibrium, which exists depending on the values of system parameters. In the absence of diffusion, our system shows rich dynamics, like Hopf bifurcation, chaos, etc. We analytically investigate the potential conditions for Turing instability in the context of diffusion. During numerical verification of our theoretical results, we see some non-stationary patterns along with the stationary pattern. By obtaining the Maximum Lyapunov exponent, we confirmed that the non-stationary pattern is chaotic. In addition, it is to be noted that maintaining ecosystem stability, preventing unpredictable population fluctuations, and ensuring the sustainability of species and resources all depend on controlling chaos in ecological models. For this purpose, we apply time-delay feedback control and successfully stabilize the spatiotemporal chaos.

Suggested Citation

  • Majee, Suvankar & Jana, Soovoojeet & R., Anand & Ramprabhakar, J., 2026. "Complex spatiotemporal dynamics in an eco-epidemic model: Turing instability, non-stationary patterns, and chaos control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 240(C), pages 650-667.
    • Handle: RePEc:eee:matcom:v:240:y:2026:i:c:p:650-667
    DOI: 10.1016/j.matcom.2025.07.057
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    References listed on IDEAS

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    1. Hossain, Mainul & Pal, Nikhil & Samanta, Sudip, 2020. "Impact of fear on an eco-epidemiological model," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. Kumar, Ajay & Kumar, Sunil, 2022. "A study on eco-epidemiological model with fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. Ghorai, Santu & Poria, Swarup, 2016. "Turing patterns induced by cross-diffusion in a predator-prey system in presence of habitat complexity," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 421-429.
    4. Pal, Pallav Jyoti & Mandal, Gourav & Guin, Lakshmi Narayan & Saha, Tapan, 2024. "Allee effect and hunting-induced bifurcation inquisition and pattern formation in a modified Leslie–Gower interacting species system," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    5. Sun Shulin & Guo Cuihua, 2013. "Dynamics of a Beddington-DeAngelis Type Predator-Prey Model with Impulsive Effect," Journal of Mathematics, Hindawi, vol. 2013, pages 1-11, December.
    6. Mukherjee, Nayana & Smith?, Stacey R. & Haque, Mainul, 2023. "Spatio-temporal patterns resulting from a predator-based disease with immune prey," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    7. Changjin Xu & Peiluan Li & Maoxin Liao, 2020. "Periodic Property and Asymptotic Behavior for a Discrete Ratio-Dependent Food-Chain System with Delays," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-12, July.
    8. Mondal, Jayanta & Samui, Piu & Chatterjee, Amar Nath, 2022. "Modelling of contact tracing in determining critical community size for infectious diseases," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    9. Yuanfu Shao & Weili Kong, 2022. "A Predator–Prey Model with Beddington–DeAngelis Functional Response and Multiple Delays in Deterministic and Stochastic Environments," Mathematics, MDPI, vol. 10(18), pages 1-25, September.
    10. Zhang, Chao & Gao, Jianguo & Sun, Hongquan & Wang, Jinliang, 2019. "Dynamics of a reaction–diffusion SVIR model in a spatial heterogeneous environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    11. Zhang, Chao & Gao, Jianguo & Sun, Hongquan & Wang, Jinliang, 2019. "Dynamics of a reaction–diffusion SVIR model in a spatial heterogeneous environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C), pages 1-1.
    12. Carfora, M.F. & Iovanna, F. & Torcicollo, I., 2025. "Turing patterns in an intraguild predator–prey model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 232(C), pages 192-210.
    13. Chakraborty, Bhaskar & Ghorai, Santu & Bairagi, Nandadulal, 2020. "Reaction-diffusion predator-prey-parasite system and spatiotemporal complexity," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    14. Liu, Junli & Liu, Bairu & Lv, Pan & Zhang, Tailei, 2021. "An eco-epidemiological model with fear effect and hunting cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    15. Sarangi, B.P. & Raw, S.N., 2023. "Dynamics of a spatially explicit eco-epidemic model with double Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 241-263.
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