Abstract
We investigate an impulsive predator-prey system with Monod-Haldane type functional response and control strategies, especially, biological and chemical controls. Conditions for the stability of the prey-free positive periodic solution and for the permanence of the system are established via the Floquet theory and comparison theorem. Numerical examples are also illustrated to substantiate mathematical results and to show that the system could give birth to various kinds of dynamical behaviors including periodic doubling, and chaotic attractor. Finally, in discussion section, we consider the dynamic behaviors of the system when the growth rate of the prey varies according to seasonal effects.
Highlights
In recent years controlling insects and other arthropods has become an increasingly complex issue
Integrated Pest Management IPM is a pest control strategy that uses an array of complementary methods: natural predators and parasites, pest-resistant varieties, cultural practices, biological controls, various physical techniques, and the strategic use of pesticides
We have studied the effects of control strategies on a predator-prey system with Monod-Haldane type functional response
Summary
In recent years controlling insects and other arthropods has become an increasingly complex issue. There are many deleterious effects associated with the use of chemicals that need to be reduced or eliminated These include human illness associated with pesticide applications, insect resistance to insecticides, contamination of soil and water, and diminution of biodiversity. It is required that we should combine pesticide efficacy tests with other ways of control Another important way to control pest populations is biological control. Natural enemies of insect pests, known as biological control agents, include predators, parasites, and pathogens. − yP x, y , y t −dy t eyP x, y , 1.1 x 0 x0 ≥ 0, y 0 y0 > 0, where x t and y t represent the population density of the prey and the predator at time t, respectively.
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