Dynamics Of Multi-Population Models Under The Influence Of Fear Effect,Light And Nutrients

In recent years,the accelerating rate of species extinction on earth is a serious challenge to human survival and development,so elucidating the key factors that influence species diversity has become a critical concern for human.In this paper,we investigate the impact of fear effect,light,and nutrients on the food chain system,the predator-prey system with multi-population in grasslands,the asymmetric competition system,and the intraguild predation system by using dynamical modeling,and clarify the roles of three factors in the conservation of species diversity.In predation systems,the fear effect cannot be ignored.We derive the predator’s functional response by using the classical Holling’s time budget argument,and formulate a three-species food chain model that incorporates both cost and benefit of the fear effect.The theoretical analysis demonstrates the dissipativity of the system as well as the existence and stability of equilibria.In combination with numerical analysis,it is observed that the fear effect can change the density of populations and shift the system from chaotic dynamics to a stable state.The modeling study indicates that fear effect is beneficial to maintain the stable coexistence of populations in the food chain system,and provides some useful biological insights for the conservation of species diversity.In grassland ecosystems,large carnivore as an important top predator that preys on both domestic and wild herbivores.A predator-prey system with multi-population which incorporates the fear effect exerted by large carnivores on herbivore foraging is developed to explore the dynamics of herbage,domestic herbivore,wild herbivore,and large carnivore.The rich dynamical behaviours of the model are well explored both analytically and numerically,such as various types of bistabilities,periodic oscillation,and chaos.In addition,the appropriate level of fear effect can not only increase the density of herbage and domestic herbivore,but also stabilize the system.The results reveal the important role of the fear effect in conserving species diversity and promoting the economic development of human.Light and nutrients are essential resources for the growth of primary producers,but they can trigger competition among populations.Pelagic and benthic producers are the basis of the whole aquatic ecosystem and compete asymmetrically for light and nutrients due to the differences in spatial ecological niches.A coupled PDE-ODE mathematical model is proposed.Several basic ecological reproductive indices are rigorously derived for pelagic producers and benthic producers by theoretical analysis,and the possible scenarios of asymmetric competition are explicitly formulated.Numerical simulations are used to investigate the effects of light,nutrients,and spatial correlation coefficients on the asymmetric competition between pelagic and benthic producers,and the results are compared with the classical resource competition theory.The study reveals that the supply balance between light and nutrients is an important condition for maintaining the coexistence of pelagic and benthic producers.Model results provide important theoretical guidance for the conservation of species diversity in aquatic ecosystems.The intraguild predation system is a complex system that involves both predation and competition,and occupies a decisive position in the composition of biological communities.Based on the ecological stoichiometry,an intraguild predation system is established to describe the dynamics of phytoplankton,zooplankton,and fish in aquatic systems,and the joint effect of light,nutrients,and fear effect on the system is investigated.Theoretical and numerical analysis results show that the appropriate range of light intensity and nutrients is beneficial to the coexistence of three populations,while excessive nutrient input can cause the system to exhibit chaotic behavior.The increase in fear level can reverse this phenomenon,as well as change the density of phytoplankton and fish populations.The results of this study provide a theoretical basis for maintaining the stability of the intraguild predation system.