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Original Articles

Global stability of equilibria

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Pages 387-397 | Received 15 Jan 2008, Accepted 03 Nov 2008, Published online: 09 Jul 2010

References

  • Aksoy , A. and Martelli , M. 2001 . Global convergence of discrete dynamical systems and forward neural networks . Turkish J. Math. , 25 : 345 – 354 .
  • H. Amann, Ordinary Differential Equations, De Gruyter Studies in Mathematics, 13, 1990
  • Bass , H. , Connell , E.H. and Wright , C. 1982 . The Jacobian conjecture: reduction of degree and formal expansion of the inverse . Bull. Amer. Math. Soc. , 7 : 287 – 330 .
  • Bruckner , A.M. 1978 . Differentiation of Real Functions , Lecture Notes in Mathematics, No. 659 Berlin/New York : Springer-Verlag .
  • Chamberland , M. 1997 . Global asymptotic stability, additive neural networks, and the Jacobian conjecture . Can. Appl. Math. Quart. , 5 : 331 – 339 .
  • Cima , A. , Essen van den , A. , Gasull , A. , Hubbers , E. and Mañosas , F. 1997 . A polynomial counterexample to the Markus–Yamabe conjecture . Adv. Math. , 131 : 453 – 457 .
  • Cima , A. , Gasull , A. and Mañosas , F. 1999 . The discrete Markus–Yamabe problem . Nonlinear Anal. , 35 : 343 – 354 .
  • Fernandes , A. , Gutierrez , C. and Rabanal , R. 2004 . Global asymptotic stability for differentiable vector fields in ℝ2 . J. Differential Equations , 206 : 470 – 482 .
  • Feßler , R. 1995 . A solution of the two-dimensional Markus–Yamabe conjecture and a generalization . Ann. Polon. Math. , 62 : 45 – 74 .
  • Furi , M. and Martelli , M. 1991 . On the mean value theorem, inequality, and inclusion . Amer. Math. Monthly , 98 : 840 – 847 .
  • Furi , M. and Martelli , M. 1994 . Strictly increasing differentiable functions . College Math. J. , 25 : 125 – 127 .
  • Gutierrez , C. 1995 . A solution of the bidemensional global asymptotic stability conjecture . Ann. Inst. H. Poincaré Anal. Non Linéaire , 12 : 627 – 671 .
  • Hartman , Ph. 1961 . On stability in the large for systems of ordinary differential equations . Can. J. Math. , 13 : 480 – 492 .
  • Hartman , Ph. and Olech , C. 1962 . On global asymptotic stability of solutions of differential equations . Trans. Amer. Math. Soc. , 104 : 154 – 178 .
  • Johnston , B. and Martelli , M. 1996 . Global attractivity and forward neural networks . Appl. Math. Lett. , 9 : 77 – 83 .
  • Keller , O.-H. 1939 . Ganze Cremona transformationen . Mon. Math. , 47 : 299 – 306 .
  • Kitchen , J.W. 1966 . Concerning the convergence of iterates to fixed points . Studia Math. , 27 : 247 – 249 .
  • La Salle , J.P. 1976 . The Stability of Dynamical Systems , Philadelphia, PA : SIAM .
  • Markus , L. and Yamabe , H. 1960 . Global stability criteria for differential systems . Osaka Math. J. , 12 : 305 – 317 .
  • Martelli , M. and Dang , M. 1994 . The derivative of a continuous nonconstant function . Appl. Math. Lett. , 7 : 81 – 84 .
  • Martelli , M. 1999 . Introduction to Discrete Dynamical Systems and Chaos , New York : Wiley .
  • Martelli , M. 1998 . Global stability of stationary states of discrete dynamical systems . Ann. Sci. Math. Québec , 22 : 201 – 212 .
  • Miller , A.D. and Vŷbornŷ , R. 1986 . Some remarks on functions with one-sided derivatives . Amer. Math. Monthly , 93 : 471 – 475 .
  • G. Prodi and A. Ambrosetti, Analisi non lineare, Scuola Normale Superiore Pisa, I Quaderno, 1973
  • Sabatini , M. 1990 . Global asymptotic stability of critical points in the plane . Rend. Sem. Mat. Univ. Politec. Torino , 48 : 97 – 103 .
  • Smith , R.A. 1981 . An index theorem and Bendixon's negative criterion for certain differential equations of higher dimension . Proc. Roy. Soc. Edinburgh Sect. A , 91 : 63 – 77 .
  • Van den Essen , A. 2000 . Polynomial Automorphisms and the Jacobian Conjecture , Boston : Birkhäuser .
  • Varberg , E.D. 1965 . On absolutely continuous functions . Amer. Math. Monthly , 72 : 831 – 841 .

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