Global boundedness and stability of solutions to a pest–natural enemy chemotaxis system

Lulu Liu; Liu Han; Dingjiang Wang; Lulu Liu; Liu Han; Dingjiang Wang

doi:10.3934/math.20261134

AIMS Mathematics

2026, Volume 11, Issue 9: 28470-28489. doi: 10.3934/math.20261134

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Research article

Global boundedness and stability of solutions to a pest–natural enemy chemotaxis system

College of Science, Xinjiang Institute of Technology, Aksu 843000, Xinjiang, China

Received: 30 June 2026 Revised: 15 August 2026 Accepted: 26 August 2026 Published: 07 September 2026
MSC : 35K55, 35Q92

Motivated by the dynamics of codling moth pests and their natural enemies in fruit forestry, this paper develops a predator–prey chemotaxis system formulated through partial differential equations. For the proposed model incorporating a Holling type Ⅰ functional response, the global boundedness of its solutions is proved via a combination of semigroup theory and energy estimates. Moreover, by constructing appropriate Lyapunov functionals, we demonstrate that under weak predation pressure, the prey-only equilibrium is globally asymptotically stable, whereas under strong predation pressure, sufficient conditions ensuring the global asymptotic stability of the positive constant equilibrium are established.
- predator–prey system,
- chemotaxis,
- global boundedness,
- local stability,
- asymptotic stability
Citation: Lulu Liu, Liu Han, Dingjiang Wang. Global boundedness and stability of solutions to a pest–natural enemy chemotaxis system[J]. AIMS Mathematics, 2026, 11(9): 28470-28489. doi: 10.3934/math.20261134

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Abstract

Motivated by the dynamics of codling moth pests and their natural enemies in fruit forestry, this paper develops a predator–prey chemotaxis system formulated through partial differential equations. For the proposed model incorporating a Holling type Ⅰ functional response, the global boundedness of its solutions is proved via a combination of semigroup theory and energy estimates. Moreover, by constructing appropriate Lyapunov functionals, we demonstrate that under weak predation pressure, the prey-only equilibrium is globally asymptotically stable, whereas under strong predation pressure, sufficient conditions ensuring the global asymptotic stability of the positive constant equilibrium are established.

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