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I am using cl_matcont to perform a bifurcation analysis of a dynamical system of ten equations (equations are identical in two blocks, thus 8 of them and 2 of them are the same)

During the continuation the toolbox finds an Hopf bifurcation having a negative lyapunov coefficient. This bifurcation gives rise to limit cycles shown in the figure I have attached. In the figure, cycles are in blue. Blue points on the curve are stable equilibrium points, while the red ones are unstable. I would like to know if the limit cycles are stable or not, but I have found two contradictory results. The negative lyapunov coefficient leads me to think about stable limit cycles (supercritical Hopf). While the orientation of the cycle and some numerical simulations lead to evident unstable limit cycles (subcritical Hopf). enter image description here Have you any suggestions to know the nature of these cycles?

Thank you in advance for any information.

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Look at the Floquet multipliers of the limit cycles. If the magnitude of all Floquet multipliers for a given limit cycle are <1, then the limit cycle is stable. If any one of the multipliers has magnitude >1, then the limit cycle is unstable. These multipliers should be saved in the last few rows of the matrix 'f' that Matcont produces when you do limit cycle continuation.

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