The simultaneous effect of chemotaxis and alarm-taxis on the global existence and stability of a predator-prey system

2025/10/16 by Shanmugasundaram, Gnanasekaran, Saha, Jitraj, Fuentes, Rafael Díaz
#35A01 #35A09 #35B40 #37N25 #65N06 #92C17 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.14728

Abstract

This study examines a fully parabolic predator-prey chemo-alarm-taxis system under homogeneous Neumann boundary conditions in a bounded domain Ω⊂ ℝⁿ with a smooth boundary ∂Ω. Under specific parameter conditions, it is shown that the system admits a unique, globally bounded classical solution. The convergence of the solution is established through the construction of an appropriate Lyapunov functional. In addition, numerical simulations are presented to validate the asymptotic behaviour of the solution. The results highlight the significant role of chemotaxis and alarm-taxis coefficients in determining the existence and stability of predator-prey models, as discussed in the literature.

Citations

• Improvement of conditions for asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity
• Aggregation vs. global diffusive behavior in the higher-dimensional Keller–Segel model

Related

• Global dynamics of a predator-prey model with alarm-taxis
• Global existence and stability in a class of chemotaxis systems with lethal interactions, nonlinear diffusion and production
• Repulsive chemotaxis and predator evasion in predator prey models with diffusion and prey taxis
• Classical and generalized solutions of an alarm-taxis model
• Global boundedness induced by asymptotically non-degenerate motility in a fully parabolic chemotaxis model with local sensing