Otro
Forced duffing oscillator
Autor
Zakia, Nasri
Binous, Housam
Resumen
Time series, phase space, Differential Equations, Poincaré section The forced Duffing oscillator exhibits behavior ranging from limit cycles to chaos due to its nonlinear dynamics. The governing equation is (d^2 x)/〖dt〗^2 +γ dx/dt-ω^2 x+ϵx^3=Γcos(Ωt), with γ=0.1, Є=0.25, ω=1, Ω=2, x(0)=1, and (dx/dt)_(t=0)=0. When the periodic force (Γ) that drives the system is large, chaotic behavior emerges and the phase space diagram is a strange attractor. In that case the behavior of the system is sensitive to the initial condition. In order to plot a Poincaré section, take one data point from phase space per period of the driving force. The Poincaré section is a complicated fractal curve when the phase diagram is a strange attractor. The Poincaré section is a single point when the phase space diagram is a limit cycle Componente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemática