Towards a bifurcation theory for nonautonomous difference equations

References

• Agarwal , R.P. 1992 . Difference Equations and Inequalities , New York : Marcel Dekker Inc. .
   Google Scholar
• Aulbach , B. 1998 . The fundamental existence theorem on invariant fiber bundles . Journal of Difference Equations and Applications , 3 : 501 – 537 .
   Google Scholar
• Aulbach , B. and Siegmund , S. 2000 . “ A spectral theory for nonautonomous difference equations ” . In Proceedings of the Fifth Conference on Difference Equations and Applications, Temuco/Chile 2000 , Gordon & Breach Publishers .
   Google Scholar
• Broer , H.W. , Huitema , G.B. , Takens , F. and Braaksma , B.L.J. 1990 . Unfoldings and Bifurcations of Quasi-Periodic Tori , No. 421 in Memoirs of the AMS Providence, Rhode Island : American Mathematical Society .
   Google Scholar
• Chow , S.-N. and Hale , J.K. 1996 . Methods of Bifurcation Theory, vol. 251 of Grundlehren der Mathematischen Wissenschaften , Berlin Heidelberg New York : Springer .
   Google Scholar
• Fabbri , R. , Johnson , R.A. and Mantellini , F. 2004 . A nonautonomous saddle-node bifurcation pattern . Stochastics and Dynamics , 4 ( 3 ) : 335 – 350 .
   Google Scholar
• Glendinning , P. 2004 . Non-smooth pitchfork bifurcations . Discrete and Continuous Dynamical Systems B , 4 ( 2 ) : 457 – 464 .
   Google Scholar
• Johnson , R.A. 1989 . Hopf bifurcation from nonperiodic solutions of differential equations. I. Linear theory . Journal of Dynamics and Differential Equations , 1 ( 2 ) : 179 – 198 .
   Google Scholar
• Johnson , R.A. , Kloeden , P.E. and Pavani , R. 2002 . Two-step transition in nonautonomous bifurcations: an explanation . Stochastics and Dynamics , 2 ( 1 ) : 67 – 92 .
   Google Scholar
• Johnson , R.A. and Mantellini , F. 2003 . A nonautonomous transcritical bifurcation problem with an application to quasi-periodic bubbles . Discrete and Continuous Dynamical Systems , 9 ( 1 ) : 209 – 224 .
   Google Scholar
• Johnson , R.A. and Yi , Y. 1994 . Hopf bifurcation from non-periodic solutions of differential equations. II . Journal of Differential Equations , 107 ( 2 ) : 310 – 340 .
   Google Scholar
• Kloeden , P.E. 2000 . Pullback attractors in nonautonomous difference equations . Journal of Difference Equations and Applications , 6 : 91 – 102 .
   Google Scholar
• Kloeden , P.E. 2004 . Pitchfork and transcritical bifurcations in systems with homogeneous nonlinearities and an almost periodic time coefficient . Communications on Pure and Applied Analysis , 3 ( 2 ) : 161 – 173 .
   Google Scholar
• Kloeden , P.E. and Siegmund , S. 2005 . Bifurcations and continuous transitions of attractors in autonomous and nonautonomous systems . International Journal of Bifurcation and Chaos , 15 ( 3 ) : 743 – 762 .
   Google Scholar
• Lang , S. 1993 . Real and Functional Analysis , New York : Springer .
   Google Scholar
• Langa , J.A. , Robinson , J.C. and Suárez , A. 2002 . Stability, instability and bifurcation phenomena in non-autonomous differential equations . Nonlinearity , 15 ( 3 ) : 887 – 903 .
   Google Scholar
• Langa, J.A., Robinson, J.C. and Suárez, A., 2006, Bifurcations in non-autonomous scalar equations, Journal of Differential Equations, 221(1), 1–35.
   Google Scholar
• Rasmussen , M. Attractivity and bifurcation for nonautonomous dynamical systems . Ph.D. Thesis . University of Augsburg .
   Google Scholar
• Wiggins , S. 1990 . Introduction to Applied Nonlinear Dynamical Systems and Chaos, vol. 2 of Texts in Applied Mathematics , New York : Springer .
   Google Scholar