scholarly journals Local integrability and linearizability of three-dimensional Lotka–Volterra systems

2012 ◽  
Vol 219 (8) ◽  
pp. 4067-4081 ◽  
Author(s):  
Waleed Aziz ◽  
Colin Christopher
Keyword(s):  
Three Dimensional ◽  
Local Integrability ◽  
Volterra Systems

Local integrability of a family of three-dimensional quadratic systems

2013 ◽  
Vol 265 ◽  
pp. 78-86 ◽  
Author(s):  
Zhaoping Hu ◽  
Maoan Han ◽  
Valery G. Romanovski
Keyword(s):  
Three Dimensional ◽  
Local Integrability ◽  
Quadratic Systems

scholarly journals Stability and Bifurcation of Two Kinds of Three-Dimensional Fractional Lotka-Volterra Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jinglei Tian ◽  
Yongguang Yu ◽  
Hu Wang
Keyword(s):  
Hopf Bifurcation ◽  
Asymptotic Stability ◽  
Theoretical Analysis ◽  
Fractional Order ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Critical Value ◽  
The Other ◽  
Bifurcation Parameter ◽  
Volterra Systems

Two kinds of three-dimensional fractional Lotka-Volterra systems are discussed. For one system, the asymptotic stability of the equilibria is analyzed by providing some sufficient conditions. And bifurcation property is investigated by choosing the fractional order as the bifurcation parameter for the other system. In particular, the critical value of the fractional order is identified at which the Hopf bifurcation may occur. Furthermore, the numerical results are presented to verify the theoretical analysis.

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