Global dynamics of a ratio-dependent predator-prey system

2001 ◽  
Vol 43 (3) ◽  
pp. 268-290 ◽  
Author(s):  
Dongmei Xiao ◽  
Shigui Ruan
Keyword(s):  
Global Dynamics ◽  
Predator Prey ◽  
Prey System ◽  
Ratio Dependent

Global dynamics of a stochastic ratio-dependent predator–prey system

2017 ◽  
Vol 10 (01) ◽  
pp. 1750002
Author(s):  
Xiaolin Fan ◽  
Zhidong Teng ◽  
Ahmadjan Muhammadhaji
Keyword(s):  
Lyapunov Functions ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Upper Bounds ◽  
Global Dynamics ◽  
Predator Prey ◽  
Prey System ◽  
Dynamical Properties ◽  
Ratio Dependent ◽  
Theoretical Results

The dynamical properties of a stochastic non-autonomous ratio-dependent predator–prey system are studied by applying the theory of stochastic differential equations, Itô’s formula and the method of Lyapunov functions. First, the existence, the uniqueness and the positivity of the solution are discussed. Second the boundedness of the moments and the upper bounds for growth rates of prey and predator are studied. Moreover, the global attractivity of the system under some a weaker sufficient conditions are investigated. Finally, the theoretical results are confirmed by the special examples and the numerical simulations.

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