, ) = s in > s 1 = ? 1 (s 2 ), one deduces ? 1 (s 2 ) > 0. Recall from Corollary 3.2.1 that one has g (s 1 ) = ? 1 (s 2 )? 2 (s 1 ) ? 1 > 0. Then the inequality ? 2 (s 1 ) > 0 is necessarily satisfied. Finally, we have shown det(J ) > 0 and tr(J ) < 0

, The wash-out equilibrium (s in , 0, s in , 0) is not necessarily hyperbolic. This explains why we cannot use the Convergence Theorem for asymptotically autonomous dynamics given in Appendix F of, vol.32

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