Book: The Duffing Equation: Nonlinear Oscillators and their Behaviour
See MMathPhys miniprojects and Duffing oscillator
More papers and references:
https://en.wikipedia.org/wiki/Intermittency
https://en.wikipedia.org/wiki/Crisis_%28dynamical_systems%29
Y. Ueda, Steady Motions Exhibited by Duffing’s Equation: A Picture Book of Regular And Chaotic Motions
Catastrophes with Indeterminate Outcome Stewart, H. B. ; Ueda, Y.
EXPLOSION OF STRANGE ATTRACTORS EXHIBITED BY DUFFING'S EQUATION - Yoshisuke Ueda
Common dynamical features on periodically driven strictly dissipative oscillators (introduces torsion and winding numbers)
Comparison of bifurcation sets of driven strictly dissipative oscillators
Wada basins
https://en.wikipedia.org/wiki/Lakes_of_Wada
Wada basin boundaries and basin cells Other link
Unpredictable behavior in the Duffing oscillator: Wada basins
Experimental investigation of the response of a harmonically excited hard Duffing oscillator From here
Analytical methods
Exact analytical solutions for forced cubic restoring force oscillator Uses Jacobi elliptic function (only for undamped Ueda oscillator I think).
A comparison of classical and high dimensional harmonic balance approaches for a Duffing oscillator
Second order averaging and bifurcations to subharmonics in duffing's equation
Subharmonic Oscillations in Nonlinear Systems
Chaotic states and routes to chaos in the forced pendulum
Organization of periodic orbits in the driven Duffing oscillator
Structure in the bifurcation diagram of the Duffing oscillator
superstructure in the bifurcation set of the duffing equation
General case of crisis-induced intermittency in the Duffing equation for double-well Duffing oscillator.
On the jump-up and jump-down frequencies of the Duffing oscillator
More books:
Chaos in Nonlinear Oscillators: Controlling and Synchronization By M Lakshmanan, K Murali
Antimonotonicity reversal of period-doubling cascades