Abstract
We describe the improved Darboux theory of integrability for polynomial ordinary differential equations in three dimensions. Using this theory and computer algebra, we study the existence of first integrals for the three-dimensional Lotka-Volterra systems. Only working up to degree two with the invariant algebraic surfaces and the exponential factors, we find the major part of the known first integrals for such systems, and in addition we find three new classes of integrability. The method used is of general interest and can be applied to any polynomial ordinary differential equations in arbitrary dimension.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
