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Dynamics of a delayed predator-prey system with stage structure and cooperation for preys

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  • Kundu, Soumen
  • Maitra, Sarit

Abstract

In this paper we have taken a delayed predator-prey system with stage structure among prey species. We assume that there is cooperation among the mature and immature preys to ensure immature prey’s existence and there is a maturation delay for immature to be mature for the preys. With this model the local stability has been discussed in presence of delay. By taking maturation delay as the key parameter, the condition for local stability has been obtained by constructing a Lyapunov functional. By taking the maturation delay as the bifurcation parameter the necessary conditions for Hopf-bifurcation have been discussed both analytically and numerically. The length of delay has been estimated to preserve the stability. Also, Lyapunov exponents have been evaluated numerically for different cases.

Suggested Citation

  • Kundu, Soumen & Maitra, Sarit, 2018. "Dynamics of a delayed predator-prey system with stage structure and cooperation for preys," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 453-460.
    • Handle: RePEc:eee:chsofr:v:114:y:2018:i:c:p:453-460
    DOI: 10.1016/j.chaos.2018.07.013
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    References listed on IDEAS

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    1. Jana, Debaldev & Agrawal, Rashmi & Upadhyay, Ranjit Kumar, 2014. "Top-predator interference and gestation delay as determinants of the dynamics of a realistic model food chain," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 50-63.
    2. Wang, Fengyan & Kuang, Yang & Ding, Changming & Zhang, Shuwen, 2013. "Stability and bifurcation of a stage-structured predator–prey model with both discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 19-27.
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    Cited by:

    1. Zhang, Zizhen & Kundu, Soumen & Tripathi, Jai Prakash & Bugalia, Sarita, 2020. "Stability and Hopf bifurcation analysis of an SVEIR epidemic model with vaccination and multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Ma, Yuanyuan & Dong, Nan & Liu, Na & Xie, Leilei, 2022. "Spatiotemporal and bifurcation characteristics of a nonlinear prey-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    3. Narayan Mondal & Dipesh Barman & Shariful Alam, 2021. "Impact of adult predator incited fear in a stage-structured prey–predator model," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 23(6), pages 9280-9307, June.
    4. Pandey, Soumik & Ghosh, Uttam & Das, Debashis & Chakraborty, Sarbani & Sarkar, Abhijit, 2024. "Rich dynamics of a delay-induced stage-structure prey–predator model with cooperative behaviour in both species and the impact of prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 49-76.

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