Subcritical period doubling in the Duffing equation-type 3 intermittency, attractor crisis

We study period doubling bifurcations, subcritical period doubling, and type 3 intermittency of the Duffing equation. The Floquet exponents of the linearization show a remarkably ordered structure and serve as a guidance of the solutions when control parameters are changed.

[1]  G. Duffing,et al.  Erzwungene Schwingungen bei veränderlicher Eigenfrequenz und ihre technische Bedeutung , 1918 .

[2]  Hamel.  Georg Duffing, Ingenieur: Erzwungene Schwingungen bei veränderlicher Eigenfrequenz und ihre technische Bedeutung. Sammlung Vieweg. Heft 41/42, Braunschweig 1918. VI+134 S , 2022 .

[3]  E. Coddington,et al.  Theory of Ordinary Differential Equations , 1955 .

[4]  A. Ostrowski.  Solution of equations and systems of equations , 1967 .

[5]  Michel Cosnard,et al.  Numerical Solution of Nonlinear Equations , 1979, TOMS.

[6]  Stability charts for Hill's equation , 1980 .

[7]  鈴木 増雄.  A. H. Nayfeh and D. T. Mook: Nonlinear Oscillations, John Wiley, New York and Chichester, 1979, xiv+704ページ, 23.5×16.5cm, 10,150円. , 1980 .

[8]  Y. Pomeau,et al.  Intermittent transition to turbulence in dissipative dynamical systems , 1980 .

[9]  P. J. Holmes,et al.  Second order averaging and bifurcations to subharmonics in duffing's equation , 1981 .

[10]  Fortunato Tito Arecchi,et al.  Hopping Mechanism Generating 1f Noise in Nonlinear Systems , 1982 .

[11]  Miguel A. Rubio,et al.  Experimental evidence of intermittencies associated with a subharmonic bifurcation , 1983 .

[12]  Kurt Wiesenfeld,et al.  Suppression of period doubling in symmetric systems , 1984 .

[13]  Werner Meyer-Ilse,et al.  Period doubling and chaotic behavior in a driven Toda oscillator , 1984 .

[14]  Hermann Haken,et al.  Attractors of convex maps with positive Schwarzian derivative in the presence of noise , 1984 .