Special cubic perturbations of the Duffing oscillator x"=x-x³ near the eight-loop

2019/07/01 by Gavrilov, Lubomir, Gargouri, Ameni, Hamed, Bassem Ben
#34C07 #37G15 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.00669

Abstract

We find an upper bound for the number of limit cycles, bifurcating from the 8-loop of the Duffing oscillator x"= x-x³ under the special cubic perturbation x"= x-x³+λ₁y+λ₂x²+λ₃xy+λ₄x²y .

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