Limit cycles for two families of cubic systems
In this paper we study the number of limit cycles of two families of cubic systems introduced in previous papers to model real phenomena. The first one is motivated by a model of star formation histories in giant spiral galaxies and the second one comes from a model of Volterra type. To prove our re...
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| Veröffentlicht in: | Nonlinear analysis 2012-12, Vol.75 (18), p.6402-6417 |
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| creator | Álvarez, M.J. Gasull, A. Prohens, R. |
| description | In this paper we study the number of limit cycles of two families of cubic systems introduced in previous papers to model real phenomena. The first one is motivated by a model of star formation histories in giant spiral galaxies and the second one comes from a model of Volterra type. To prove our results we develop a new criterion on the non-existence of periodic orbits and we extend a well-known criterion on the uniqueness of limit cycles due to Kuang and Freedman. Both results allow to reduce the problem to the control of the sign of certain functions that are treated by algebraic tools. Moreover, in both cases, we prove that when the limit cycles exist they are non-algebraic. |
| doi_str_mv | 10.1016/j.na.2012.07.012 |
| format | Article |
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| language | eng |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Algebra Bifurcation Criteria Cubic system Kolmogorov system Limit cycle Mathematical models Nonlinearity Orbits Spiral galaxies Star formation Uniqueness |
| title | Limit cycles for two families of cubic systems |
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