Dynamics of a predator-prey model with Gompertz growth and mutual interference

Ningxia’s unique climate produces high-medicinal-value goji berry (Lycium barbarum L.), yet expanding cultivation faces severe threats from Aphis gossypii Glover (Hemiptera: Aphididae). As chemical control compromises medicinal quality through pesticide residues, developing effective biological control is critical for sustainable production. This study establishes a dynamical model incorporating Gompertz growth and mutual interference between A. gossypii and its natural enemy Coccinella undecimpunctata Linnaeus (Coleoptera: Coccinellidae), employing qualitative analysis to investigate equilibrium stability and bifurcation behaviors. Results demonstrate an unstable boundary equilibrium and up to three positive equilibria exhibiting saddle characteristics, stable/unstable foci/nodes, and limit cycles, with rich dynamics including super/sub-critical Hopf and Bogdanov-Takens bifurcations. Also, numerical simulations validate these complex dynamical behaviors. For practical application, findings suggest maintaining moderate predator release to sustain low aphid populations, whereas excessive release causes short-term suppression followed by severe rebound due to predator starvation, offering specific quantitative criteria for optimizing field biological control strategies.