Abstract
This article examines the interaction between prey populations, juvenile predators, and adult predators. A mathematical model that considers adding food and anti-predators was developed. The equilibria of the existing system are that the system has four equilibria points with conditions suitable for the locale. Numerical simulations were carried out to describe the dynamics of the system solution. Based on numerical simulations, the varying of parameter causes changes in the extinction of prey or survival of prey populations, juvenile predators, and adult predators. Addfood parameters (A) encourae Hopf Bifurcation and Saddle-node bifurcation Numerical continuity results show that Hopf bifurcation occurs when the parameter value A = 1.00162435 and when the parameter value A = 2.435303 Saddle-node bifurcation occurs.
Highlights
The phenomena in ecology, especially in agriculture are interesting to study
Based on the background of several studies of prey-predator models, we developed a one prey-two predators’ model to provide an overview of the dynamics of change through numerical simulations
In this paper we evolve of the prey population, juvenile predators, and adult predators model to delve the dynamics and incoporates addfood and anti-predator defense
Summary
The phenomena in ecology, especially in agriculture are interesting to study. Pests are plant-disturbing organisms ranging from roots, stems, and leaves. Planthonppers or insects are one of the pests for plants that can damage crops. Dragonflies can be used by farmers to control various pests, especially in rice fields. An adult dragonfly can consume hundreds of leafhoppers every day [1]. Juvenile that lives in water prey on leafhoppers or small insects. Adult dragonflies will eat on the other pests on the surface of the water ranging from leafhoppers to insects. The phenomenon of natural enemies can affect the development of pest populations, thereby protecting crops from damage and crop failure. The reduction in the number of pests makes dragonfly as predator look for alternative food other than leafthoppers. Additional food is needed to keep adult predatory species from becoming extinct so that the balance between pest and both of predator species is controlled [2]. Model [10] discusses the Rosenzweig-MacAthur model with the
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