Fig 1.
Graphical illustration of three-wave solution (9) in x − y plane when a2 = 0.1, a3 = 0.2, j1 = 0.16, j2 = 1, j3 = 0.04, k2 = k3 = m1 = m2 = m3 = 1, α = 0.21, β = −0.1, σ1 = 2.2, σ3 = 0.11, σ4 = −4.1.
Fig 2.
The phase portraits of Hamiltonian saddle-node bifurcation.
Fig 3.
Phase portraits of periodic and quasi-periodic behavior in perturbed dynamical system (40) using initial condition (0.5, 0, 0.5) and d1 = 2, d2 = 1.5, ω = 4.5.
Fig 4.
Poincare section for perturbed dynamical system (40) at initial condition (0.5, 0, 0.5) and d1 = 2, d2 = 1.5, w = 4.5.
Fig 5.
Time series analysis of perturbed dynamical system (40) using initial condition (0.5, 0, 0.5) and d1 = 2, d2 = 1.5, ω = 4.5.
Fig 6.
Dynamics of Lyapunov exponent for perturbed dynamical system (40) using time span [0, 100] and d1 = 2, d2 = 0.5, w = 4.5.
Fig 7.
Sensitive analysis of dynamical system (36) for initial conditions (ϕ, v) = (0.1, 0) in red color, (ϕ, v) = (0.2, 0) in navy blue color and (ϕ, v) = (0.3, 0) in green color.
Table 1.
Computation of Lyapunov exponent values for perturbed dynamical system (40) using time span [0, 100] and d1 = 2, d2 = 0.5, w = 4.5 (a) g0 = 0.5 and (b) g0 = 2.5.