I would like to check these nonlinear differential equations whether consist limit cycle or not.
X1’= (d*E/L)-(1/L)*x2
X2’= (1/C)*x1-P/(C*x2)
Truly Yours
Dear Mustafa,
You may want to check Poicaré-Bendixon's theorem that provides results for 2D systems (your case)...
https://en.m.wikipedia.org/wiki/Poincaré–Bendixson_theorem
As far asI know there is no equivalent result for 3D systems.
Dear Mustafa Alrayah Hassan Ibraheem:
Please also check my paper "Construction of Dulac functions for mathematical models in population biology". We propose a method for the construction of Dulac function to rule out the existence of periodic orbits
You can download it from this link: https://www.researchgate.net/publication/269396259_Construction_of_Dulac_functions_for_mathematical_models_in_population_biology
If you use the Bendixson criterion, it is clear that the system does not support periodic orbits.
Best regards
Cruz
Article Construction of Dulac functions for mathematical models in p...
I agreed with Prof. Aguirre, check the Poicaré-Bendixon's theorem.
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