Fractional and stochastic dynamics of predator–prey systems: The role of fear and global warming

Abstract

This study introduces a predator–prey model incorporating fear of predators, memory effects and the influences of climate changes. Climate change influences are represented through an exponential decay function. We examine the well-posedness of the system by analyzing the existence, uniqueness, boundedness, and positivity of its solutions. Additionally, the local dynamics of the system are analyzed, with a specific focus on the occurrence of Hopf bifurcation. The effects of environmental disturbances on system dynamics are also examined through white noises. Numerical explorations include sensitivity of the parameters as well as one/two-parameter bifurcation diagrams. Our results explore the interactive effects of the prey’s birth rate and the fear of predators. Lower values for either parameter make it challenging to achieve stability, even if the value of the other parameter is high. Moreover, when fear levels become excessively high, stability can be regained only if the prey’s birth rate is sufficiently increased. Overall, our study provides deep insights into the influence of fear, fractional-order dynamics, and climate change effects on the predator–prey interactions.