Sammendrag
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.
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