非线性方程组求解

hlxu830

u1=0.01
u2=0.02
beta13=-0.82
beta14=0.55
beta11=-0.003
beta5=0.9
beta16=6.55
beta22=-0.82
beta21=-0.001
beta24=0.5
sigma2=6.5
f1=8
syms x1 x2 x3 x4
sigma1=[-10:0.1:10]
A=-u1*x1+(-0.5*sigma1+0.125*(f1^2)*beta14)*x2-0.5*beta13*x3-0.5*beta11*x4-0.125*beta5*x2*(x3^2)-0.375*beta5*x2*(x4^2)-0.375*beta5*x2*(x1^2)-0.375*beta5*(x2^3)-0.25*beta5*x1*x3*x4-0.5*beta16*f1
B=(0.5*sigma1-0.375*(f1^2)*beta14)*x1-u1*x2+0.5*beta11*x3-0.5*beta13*x4+0.375*beta5*x1*(x3^2)+0.125*beta5*x1*(x4^2)+0.375*beta5*x1*(x2^2)+0.375*beta5*(x1^3)+0.25*beta5*x2*x3*x4
C=-0.5*beta22*x1-0.5*beta22*x2-u2*x3+(-0.5*sigma2-0.125*(f1^2)*beta24)*x4-0.125*beta5*(x1^2)*x4-0.375*beta5*(x2^2)*x4-0.375*beta5*(x3^2)*x4-0.375*beta5*(x4^3)-0.25*beta5*x1*x2*x3
D=0.5*beta21*x1-0.5*beta22*x2+(0.5*sigma2-0.375*(f1^2)*beta24)*x3-u2*x4+0.375*beta5*(x1^2)*x3-0.125*beta5*(x2^2)*x3+0.375*beta5*x3*(x4^2)+0.375*beta5*(x3^3)+0.25*beta5*x1*x2*x4
Y2=[0 0 0 0]
Y1=[A B C D]
Y1=Y2
fsolve

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各位大侠，我是初学者，很多地方不懂。请问上面的方程怎么求解?谢谢！

huwenhua

回复 1 # hlxu830 的帖子

你好，我画两自由度幅频响应时也在为这个问题纠结，试过matalab的fsolve，但变sigma时x的初值不知道该怎么选，得出的X的数值解基本不行，画出的响应曲线很不光滑。试过BFS和newton法之类，但迭代几次后出现除以零的情况，试过用maple求极坐标的解析解，但还是画不出常见的软或硬弹簧特性图。不知道你的这个问题解决了没有，如果你有新的好办法，能不能给我留言？