Period-doubling bifurcation and harvesting control: prey-predator-scavenger system with additional food and fear effects

Le résumé fourni par la source

Ecological systems are often influenced simultaneously by predation, scavenging behavior, fear-induced responses, and harvesting activities, all of which play important roles in species persistence and resource management. While these mechanisms have been extensively studied individually, their combined effects on ecosystem stability, biodiversity conservation, and optimal harvesting policies remain largely unexplored. To address this gap, a three-species prey–predator–scavenger model is proposed and analyzed, incorporating a Crowley–Martin functional response, the supply of additional food for the predator, and a double fear effect induced by both predator and scavenger populations on prey growth. The scavenger population consumes living prey and predator carcasses, and combined quadratic harvesting is imposed on both predator and scavenger populations. The mathematical properties of the model, including positivity, boundedness, permanence, and uniform persistence, are established under suitable conditions. The local dynamics of all biologically feasible equilibrium points are investigated, and the occurrence of transcritical and Hopf bifurcations is characterized using Sotomayor’s theorem and Liu’s criterion, respectively. The analysis reveals the existence of multiple Hopf bifurcation points, leading to stability switches as key parameters vary. Numerical simulations further demonstrate the emergence of complex dynamics through period-doubling bifurcations and chaos. To explore sustainable resource utilization, an optimal harvesting problem is formulated and solved using Pontryagin’s Maximum Principle. The impacts of harvesting efforts, discount rates, and fear intensity on both population dynamics and economic returns are systematically examined. The results demonstrate that scavenging interactions, fear effects, and harvesting strategies play a combined role in ecosystem stability and long-term species coexistence. The proposed framework provides valuable insights for designing harvesting policies that balance economic profitability with biodiversity conservation and sustainable ecosystem management.

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