On the zero-Hopf bifurcation of the Lotka-Volterra systems in R3
Here we study the Lotka-Volterra systems in R3, i.e. the differential systems of the form dxi/dt = xi(ri - Σ3j=1 aijxj), i = 1, 2, 3. It is known that some of these differential systems can have at least four periodic orbits bifurcating from one of their equilibrium points. Here we prove that there...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2020 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:232162 |
| Online Access: | https://ddd.uab.cat/record/232162 https://dx.doi.org/urn:doi:10.3390/math8071137 |
| Access Level: | Open access |
| Keyword: | Lotka-Volterra polynomial differential systems Periodic orbit Hopf bifurcation Averaging theory |
| Summary: | Here we study the Lotka-Volterra systems in R3, i.e. the differential systems of the form dxi/dt = xi(ri - Σ3j=1 aijxj), i = 1, 2, 3. It is known that some of these differential systems can have at least four periodic orbits bifurcating from one of their equilibrium points. Here we prove that there are some of these differential systems exhibiting at least six periodic orbits bifurcating from one of their equilibrium points. The tool for proving this result is the averaging theory of third order. |
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