Stable and Unstable Regions of the $\delta$-$\varepsilon$ plane.Curves corresponding to expansions of larger periods: curves with $2\pi$-periodic solutions (black solid and black dashed), curves with $4\pi$-periodic solutions (orange solid and orange dashed), curves with $8\pi$-periodic solutions (red dashed) and curves with $16\pi$-periodic solutions (blue dashed).The width of the $5$th stable band.$1$st stable band, $a=0.2278,b=-0.09431,c=1.994$$2$nd stable band, $a=1.390,b=0.8504,c=1.24$$3$rd stable band, $a=6.045,b=3.674,c=0.9081$$4$th stable band, $a=20.17,b=2.507,c=0.6972$$5$th stable curve, $a=56.06,b=23.20,c=0.5527$$6$th stable band, $a=136.8,b=12.38,c=0.4496$$7$th stable band, $a=303.0,b=20.39,c=0.374$$8$th stable band, $a=623.9,b=164.2,c=0.3168$$9$th stable band, $a=1212,b=283.9,c=0.2726$$10$th stable curve, $a=2248,b=473.9,c=0.2377$The triangle area corresponding to $R_{w_1}$. The green area is the stable region, and shaded area is the unstable region.The triangle area corresponding to $R_{w_2}$. The green area is the stable region, and shaded area is the unstable region.The triangle area corresponding to $R_{w_3}$. The green area is the stable region, and shaded area is the unstable region.The triangle area corresponding to $R_{w_4}$. The green area is the stable region, and shaded area is the unstable region.Probabilities $P_i$ and the fitting curve.Normalized solutions corresponding to $p(\sin t,0)$ (solid black), $p(\sin t,5)$ (red), $p(\sin t,10)$ (orange), $p(\sin t,20)$ (green), $p(\sin t,40)$ (blue), $p(\sin t,80)$ (purple).Normalized solutions corresponding to $p(\sin 2t,0)$ (solid black), $p(\sin 2t,5)$ (red), $p(\sin 2t,10)$ (orange), $p(\sin 2t,20)$ (green), $p(\sin 2t,40)$ (blue), $p(\sin 2t,80)$ (purple).Normalized solutions corresponding to $p(\sin 3t,0)$ (solid black), $p(\sin 3t,5)$ (red), $p(\sin 3t,10)$ (orange), $p(\sin 3t,20)$ (green), $p(\sin 3t,40)$ (blue), $p(\sin 3t,80)$ (purple).$t$-position of maximal point on curve $p(\sin t,\varepsilon)$, with $a=3.031,b=5.736,c=10.18,d=14.88$.$t$-position of maximal point on curve $p(\sin 2t,\varepsilon)$, with $a=10.31,b=22.8,c=17.43,d=29.09$.$t$-position of maximal point on curve $p(\sin 3t,\varepsilon)$, with $a=432.5,b=1345,c=607.2,d=1257$. \caption{t-position of maximal points, with fitting curve $t=\frac{a\varepsilon+b}{\varepsilon^2+c\varepsilon+d}$. $t$-position of the second maximal point on curve $p(\sin 2t,\varepsilon)$, with $a=2.272,b=4.602,c=12.75,d=19.84$.$t$-position of the second maximal point on curve $p(\sin 3t,\varepsilon)$, with $a=710.8.5,b=1894,c=5324,d=1.045\times 10^4$.t-position of the third maximal points on curve $p(\sin 3t,\varepsilon)$, with fitting curve $t=\frac{a\varepsilon+b}{\varepsilon^2+c\varepsilon+d}$, $a=9.567,b=23.07,c=22.86,d=40.46$.u-position of the second maximal points on curve $p(\sin 2t,\varepsilon)$, with fitting curve $t=\frac{a\varepsilon^2+b\varepsilon+c}{\varepsilon^2+d\varepsilon+e}$. $a=0.8393,b=-0.5638,c=5.566,d=-0.1973,e=5.571$.$u$-position of the second maximal point on curve $p(\sin 3t,\varepsilon)$, with $a=0.7784,b=-3.71,c=21.57,d=150,e=-3.899,f=30.57,g=149.9$.$u$-position of the third maximal point on curve $p(\sin 3t,\varepsilon)$, with $a=0.8166,b=-4.106,c=20.44,d=136.9,e=-4.234,f=25.11,g=136.8$.Normalized solutions corresponding to $p(\cos 0t,\varepsilon)$, with $\varepsilon=0,1,2,3,4,5,10,20,40,80,160$.Normalized solutions corresponding to $p(\cos t,\varepsilon)$, with $\varepsilon=0,1,2,3,4,5,10$.Normalized solutions corresponding to $p(\cos t,\varepsilon)$, with $\varepsilon=10,20,40,80,160$.Normalized solutions corresponding to $p(\cos 2t,\varepsilon)$, with $\varepsilon=0,1,2,3,4,5,6$.Normalized solutions corresponding to $p(\cos 2t,\varepsilon)$, with $\varepsilon=6,7,8,9,10,20,30,40,60,80,100,160$.The $u$ coordinate of minimum points of solutions for points $p(\cos 0,\varepsilon)$, with $\varepsilon=0,1,\cdots, 200$. Fitting curve $u=\frac{a\varepsilon+b}{\varepsilon^2+c\varepsilon+d}$, with $a=-0.02171,b=0.2895,c=0.2289,d=0.2895$.The $t$ coordinate of minimum points of solutions for points $p(\cos t,\varepsilon)$, with $\varepsilon=2,\cdots, 200$. Fitting curve $y=\frac{a\varepsilon+b}{\varepsilon^2+c\varepsilon+d}$, with $a=241,9,b=1284,c=310.8,d=177.1$.The $u$ coordinate of minimum points of solutions for points $p(\cos t,\varepsilon)$, with $\varepsilon=0,1,2,\cdots, 200$. Fitting curve $u=\frac{a\varepsilon^2+b\varepsilon+c}{\varepsilon^2+d\varepsilon+e}$, with $a=0.8687,b=-1.631,c=0.8498,d=-1.72$ and $e=0.8497$.The $u$ coordinate of minimum points of solutions for points $p(\cos t,\varepsilon)$, with $\varepsilon=0,1,2,\cdots, 200$. Fitting curve $u=\frac{a\varepsilon+b}{\varepsilon^2+c\varepsilon+d}$, with $a=0.2495,b=-4.991,c=-3.037,d=6.722$.The $u$ coordinate of minimum points of solutions for points $p(\cos t,\varepsilon)$, with $\varepsilon=0,1,2,\cdots, 200$. Fitting curve $u=\frac{a\varepsilon+b}{\varepsilon^2+c\varepsilon+d}$, with $a=0.2495,b=-4.991,c=-3.037,d=6.722$.The $t$ coordinate of maximum points of solutions for points $p(\cos 2t,\varepsilon)$, with $\varepsilon=5,6,\cdots, 200$. Fitting curve $t=\frac{a\varepsilon^2+b\varepsilon+c}{\varepsilon^2+d\varepsilon+e}$, with $a=0.5572,b=88.5,c=-3.009,d=55.35$ and $e=-157.7$.The $t$ coordinate of the second peak of solutions for points $p(\cos 2t,\varepsilon)$, with $\varepsilon=5,6,\cdots, 200$. Fitting curve $t=\frac{a\varepsilon^2+b\varepsilon+c}{\varepsilon^3+d\varepsilon^2+e\varepsilon+f}$, with $a=269.3,b=4745,c=-9715,d=641.3,e=-2040$ and $f=-6017$.The $t$ coordinate of the second peak of solutions for points $p(\cos 2t,\varepsilon)$, with $\varepsilon=1,2,\cdots, 200$. Fitting curve $t=\frac{a\varepsilon^3+b\varepsilon^2+c\varepsilon+d}{\varepsilon^3+e\varepsilon^2+f\varepsilon+g}$, with $a=0.7931,b=-4.642,c=6.596,d=13.45,e=--5.508,f=9.829$ and $g=13.44$.The $t$ coordinate of the second peak of solutions for points $p(\cos 2t,\varepsilon)$, with $\varepsilon=1,2,\cdots, 200$. Fitting curve $y=\frac{a\varepsilon^2+b\varepsilon+c}{\varepsilon^2+e\varepsilon+f}$, with $a=-0.006875,b=0.7009,c=-8.537,d=-2.457,e=8.857$.The $t$ coordinate of the second peak of solutions for points $p(\cos 2t,\varepsilon)$, with $\varepsilon=5,6,\cdots, 200$. Fitting curve $y=\frac{a\varepsilon^2+b\varepsilon+c}{\varepsilon^3+d\varepsilon^2+e\varepsilon+f}$, with $a=0.2268,b=-25.1,c=587.7,d=4.775,e=-156$ and $f=1002$.Normalized solutions corresponding to $p(\sin \frac12t,\varepsilon)$, with $\varepsilon=0,1,2,3,4,5,10,20,40,80,160$.Normalized solutions corresponding to $p(\sin\frac32t,\varepsilon)$, with $\varepsilon=0,5,10,20,40,80,160$.Normalized solutions corresponding to $p(\cos \frac12t,\varepsilon)$, with $\varepsilon=0,1,2,3,4,5,10,20,40,80,160$.Normalized solutions corresponding to $p(\cos \frac32t,\varepsilon)$, with $\varepsilon=0,1,2,3,4,5,10,20,40,80,160$.
