Dynamics of an aquatic diffusive predator–prey model with double Allee effect and [formula omitted]-dependent capture rate

Abstract

To investigate ocean acidification and Allee effects on the dynamics of a marine predator–prey system, an aquatic diffusive predator–prey model with double Allee effect on prey and pH-dependent capture rate is considered. First, we study the stability of constant steady state solutions using linearized theory. Second, the nonexistence of nonconstant positive steady state solutions is shown for appropriate ranges of parameters. Furthermore, we show the existence of a Hopf bifurcation and derive the direction and stability of the bifurcating periodic solutions. Both theoretical analysis and numerical simulation show that changing predator–prey interaction strengths, due to changing environmental conditions, can fundamentally change the system dynamics, even for apparently small changes in interaction strength. As the interaction strength decreases due to decreasing ocean pH, the system dynamics transition from persistent fluctuations in species abundances (periodic solutions), to stable coexistence, to predator extinct (with stable non-zero prey abundance), suggesting the potential for ocean acidification to decrease the abundance and diversity of marine species by weakening predation rates. Moreover, double Allee effect parameters together determine the stability of periodic solutions when the spatially homogeneous bifurcating periodic solutions exist, and the wavelength becomes longer as the Allee effect increases.