Stochastic layer of Duffing's equation near its subharmonic resonant orbit (Q1912953)

The stochastic layer of Duffing's equation based on the chosen resonance is investigated. For non-dissipative Duffing's equation, two critical conditions are obtained when its global stochastic layer occurs and vanishes for the given resonance. In addition, a limit critical condition has been presented when all possible resonances exist in the stochastic layer. Our results are compared with the critical conditions resulting from both Chirikov overlap method and renormalization techniques. Finally, using the critical conditions, numerical simulations are performed to check our theoretical predictions of the stochastic layer based on the given resonance.