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Abstract
In this paper, we propose a new multiple-prey one-predator continuous time nonlinear system model, in which the number of teams of preys is equal to 3; namely, a continuous time three-prey one-predator model is put forward and studied. The fourth-order differential equation is established, in which the prey teams help each other. The equilibrium points and stability are analyzed. When not considering preys help each other, we study the global stability and persistence of the model without help terms. The simulation results of system solutions with help terms corresponding to locally asymptotically stable equilibrium points and without help terms corresponding to globally asymptotically stable equilibrium points are given.
Highlights
Nonlinear systems exist in many ways with various research directions, such as chaotic circuit [1,2,3,4,5,6,7,8], neural network [9,10,11,12,13,14,15], and image encryption [16,17,18]
In 1965, Holling proposed the functional responses of three different species to simulate predation. ese functional responses describe how predators transform the captured prey into their own growth
The prey-predator model can be divided into four categories: (i) the first category is the single-prey single-predator model; (ii) the second category is the single-prey multipredator model; (iii) the third category is the multiprey multipredator model; and (iv) the fourth category is the multiprey single-predator model. ere are many research studies on the first type of the model
Summary
Nonlinear systems exist in many ways with various research directions, such as chaotic circuit [1,2,3,4,5,6,7,8], neural network [9,10,11,12,13,14,15], and image encryption [16,17,18]. Wang and Jing [22] studied the global stability and the existence of limit cycles of a predator-prey system. Rough the theoretical analysis of the equations, the necessary and sufficient conditions for the existence of the exclusion principle were obtained, and the global dynamic behaviors of the three species in the first octaves were given. For the fourth category model, Elettreby [28] proposed a two-prey onepredator model, in which the prey teams help each other. No continuous time multiple-prey onepredator model in which the number of teams of preys is greater than 2 has been proposed. Erefore, in this paper, we propose a new multiple-prey one-predator model, in which the number of teams of preys is equal to 3; namely, a continuous time three-prey onepredator model is put forward and studied. Erefore, in this paper, we propose a new multiple-prey one-predator model, in which the number of teams of preys is equal to 3; namely, a continuous time three-prey onepredator model is put forward and studied. e fourth-order differential equation is established. e equilibrium points and stability are analyzed
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