Dynamics of a detrital-based mangrove food chain system driven by Holling type Ⅱ functional response and intraspecific competition

Hanqi Zhu; Yan Yan; Hanqi Zhu; Yan Yan

doi:10.3934/math.2025692

AIMS Mathematics

2025, Volume 10, Issue 7: 15433-15456. doi: 10.3934/math.2025692

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Research article

Dynamics of a detrital-based mangrove food chain system driven by Holling type Ⅱ functional response and intraspecific competition

Hanqi Zhu ,
Yan Yan ^,

Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Received: 14 February 2025 Revised: 26 May 2025 Accepted: 11 June 2025 Published: 04 July 2025
MSC : 34K18, 37N25, 92B05

In this paper, we propose a detrital-based mangrove food chain system with Holling type Ⅱ functional response, intraspecific competition, and delay effects. First, we prove the solution of this system is positive and bounded with the positive initial conditions. Second, we calculate the equilibria and investigate the asymptotical stability of equilibria with and without delays. Then, by taking the delay as the bifurcation parameter and using bifurcation theory, the bifurcation conditions for the system to undergo Hopf bifurcation at the interior equilibrium point are obtained. Furthermore, we also conduct the length estimation of delay to preserve the stability by using the Nyquist criterion. Finally, with the suitable choices of the parameters, numerical simulations have been carried out to substantiate our analytical results.
- detrital food chain system,
- stability,
- Hopf bifurcation,
- Nyquist criteria,
- delay length estimation
Citation: Hanqi Zhu, Yan Yan. Dynamics of a detrital-based mangrove food chain system driven by Holling type Ⅱ functional response and intraspecific competition[J]. AIMS Mathematics, 2025, 10(7): 15433-15456. doi: 10.3934/math.2025692

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Abstract

In this paper, we propose a detrital-based mangrove food chain system with Holling type Ⅱ functional response, intraspecific competition, and delay effects. First, we prove the solution of this system is positive and bounded with the positive initial conditions. Second, we calculate the equilibria and investigate the asymptotical stability of equilibria with and without delays. Then, by taking the delay as the bifurcation parameter and using bifurcation theory, the bifurcation conditions for the system to undergo Hopf bifurcation at the interior equilibrium point are obtained. Furthermore, we also conduct the length estimation of delay to preserve the stability by using the Nyquist criterion. Finally, with the suitable choices of the parameters, numerical simulations have been carried out to substantiate our analytical results.

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