Fig 1.
The comparative profile of solution u1(x,t) for different values of α using 3D and 2D plots.
Fig 2.
The comparative profile of solution u2(x,t) for different values of α using 3D and 2D plots.
Fig 3.
The comparative profile of solution u5(x,t) for different values of α using 3D and 2D plots.
Fig 4.
The comparative profile of solution u12(x,t) for different values of α using 3D and 2D plots.
Fig 5.
The comparative profile of solution u18(x,t) for different values of α using 3D and 2D plots.
Fig 6.
The comparative profile of solution u20(x,t) for different values of α using 3D and 2D plots.
Fig 7.
The comparative profile of solution u22(x,t) for different values of α using 3D and 2D plots.
Fig 8.
The comparative profile of solution u29(x,t) for different values of α using 3D and 2D plots.
Fig 9.
The comparative profile of solution u29(x,t) for different values of α using 3D and 2D plots.
Fig 10.
The comparative profile of solution u31(x,t) for different values of α using 3D and 2D plots.
Fig 11.
The comparative profile of solution u56(x,t) for different values of α using 3D and 2D plots.
Fig 12.
Graphical visualization of case 1 under the parametric value k= 1, b=1 and , s1 = 3.
Fig 13.
Graphical visualization of case 2 under the parametric value k= 1, b=1 and , s1 = 3.
Fig 14.
Graphical visualization of case 3 under the parametric value k= 1, b=1 and , s1 = 3.
Fig 15.
Graphical visualization of case 4 under the parametric value k = 1, b = 1 and , s1 = 3.
Fig 16.
Physical illustration the 2D and 3D chaotic behavior of system (77) under specific parameter values N1 = 0.5, N2 = 0.5, ,
.
Fig 17.
Physical illustration the 2D and 3D chaotic behavior of system (77) under specific parameter values N1 = 0.5, N2 = 0.2, ,
.
Fig 18.
Physical visualization of time series behavior of system (77), at initial condition 0.01, 0.1, 0.1, illustrate different color curves respectively with N1 = 0.3, N2 = 0.3, = 0.5,
.
Fig 19.
Physical visualization of time series behavior of system (77), at initial condition 0.1, 0.01, 0.1, illustrate different color curves respectively and the parametric values are N1 = 0.03, N2 = 0.07, = 0.001,
.
Fig 20.
A physical interpretation of the Lyapunov exponent highlights the presence of chaos when certain parameter values are applied N1 = 0.9, N2 = 0.8, = 0.01,
.