Dynamics of a state feedback impulsive predator-prey model incorporating fear effect and additional food supply

Meng Zhang; Jiayi Zheng; Meng Zhang; Jiayi Zheng

doi:10.3934/era.2026155

Electronic Research Archive

2026, Volume 34, Issue 5: 3481-3502. doi: 10.3934/era.2026155

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Dynamics of a state feedback impulsive predator-prey model incorporating fear effect and additional food supply

Meng Zhang ^,,
Jiayi Zheng

School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, China

Received: 15 February 2026 Revised: 08 April 2026 Accepted: 13 April 2026 Published: 22 April 2026

This study proposes a predator-prey model that incorporates fear effects and additional food provision. A theoretical analysis is conducted by first establishing the positivity and boundedness of solutions, and then examining the existence and stability of all feasible equilibria. Models with unilateral and bilateral impulsive state feedback control are further introduced and analyzed. For these controlled systems, sufficient conditions for the existence and orbital asymptotic stability of order-1 periodic solutions are derived. Numerical simulations are provided to support the theoretical findings, showing excellent agreement with the analytical results. Finally, a systematic sensitivity analysis is performed to quantify the influence of the prey's fear factor and the total amount of additional food on the system dynamics.
- fear,
- additional food,
- predator-prey model,
- successor function,
- order-1 periodic solution
Citation: Meng Zhang, Jiayi Zheng. Dynamics of a state feedback impulsive predator-prey model incorporating fear effect and additional food supply[J]. Electronic Research Archive, 2026, 34(5): 3481-3502. doi: 10.3934/era.2026155

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Abstract

This study proposes a predator-prey model that incorporates fear effects and additional food provision. A theoretical analysis is conducted by first establishing the positivity and boundedness of solutions, and then examining the existence and stability of all feasible equilibria. Models with unilateral and bilateral impulsive state feedback control are further introduced and analyzed. For these controlled systems, sufficient conditions for the existence and orbital asymptotic stability of order-1 periodic solutions are derived. Numerical simulations are provided to support the theoretical findings, showing excellent agreement with the analytical results. Finally, a systematic sensitivity analysis is performed to quantify the influence of the prey's fear factor and the total amount of additional food on the system dynamics.

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