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.