We characterize the integrability and the non-existence of periodic orbits for the 2-dimensional Kolmogorov systems of the formxÌ‡=x( Pn(x,y)+Rm(x,y)),yÌ‡=y(Qn(x,y) +Rm(x,y)),where n and m are positive integers and Pn, Qn and Rm are homogeneous polynomials of degree n,n and m, respectively. © 2013 Elsevier Inc. All rights reserved.
|Journal||Applied Mathematics and Computation|
|Publication status||Published - 29 Oct 2013|
- Kolmogorov systems
- Lotka-Volterra systems
- Periodic orbits