Stability and bifurcation analysis in a novel discrete prey-predator system incorporating moonlight, water availability, and vigilance effects

Abstract

Abstract This study explores the dynamics of a discrete-time predator–prey model derived from a continuous framework, integrating factors such as prey vigilance, refuge availability, water resources, and moonlight. The model captures realistic ecological scenarios where vigilance reduces predation success but also incurs energetic and temporal costs, leading to diminished prey population growth. Additionally, mammalian prey consumption is influenced by the availability of refuge, water resources, and moonlight intensity, reflecting key environmental and behavioral factors. The analysis examines the boundedness of solutions, the stability and existence of fixed points, and the emergence of bifurcations. The study emphasizes codimensionone bifurcations, including Neimark–Sacker bifurcations, and codimension-two bifurcations, such as 1:2 resonance. Detailed numerical simulations are employed to investigate the complex dynamics arising from these bifurcations, providing significant insights into the model’s behavior. The findings contribute to a deeper understanding of how ecological and environmental factors interact in predator–prey systems and their implications for ecosystem stability.