Limit cycles for two families of cubic systems
The authors study the number of limit cycles of two families of cubic systems representing models of real phenomena. The first one has the form \[ \dot{x}=A(1-x-y)-B xy^2, \;\;\dot{y}=-y(1-x-y)+Bxy^2, \] where \(A\) and \(B\) are positive real parameters. It is motivated by a model of star formation histories in giant spiral galaxies. The second one comes from a model of Volterra type and has the form \[ \dot{x}=x(x(1-x)-(x+n)y), \;\;\dot{y}=y(x+n)(x-m), \] where \(m\) and \(n\) are positive real parameters. To prove the main results on the existence of periodic orbits, the authors extend a criterion on the uniqueness of limit cycles due to Kuang and Freedman and construct of a suitable Dulac function.
scientific article; zbMATH DE number 6092713
scientific article