非线性动力系统之二阶系统习题
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x ' = x + y + - x (x 2 + y 2) y ' = - 2 x + y - y (x 2 + y 2) 10 8 6 4 2 0 -2 -4 -6 -8 -10 -10 -8 -6 -4 -2 0 x 2 4 6 8 10
y
(2) >> syms x y >> [x y]=solve('y=0','-x+y*(2-3*x^2-2*y^2)=0'); >> [x y] ans = [ 0, 0] (3) >> syms x y [x y]=solve('y=0','-x+y-2*(x+2*y)*y^2=0'); >> [x y] ans = [ 0, 0]
非线性二阶系统例题习题
>> syms x y >> [x y]=solve('x+y-x*(x^2+y^2)=0','-2*x+y-y*(x^2+y^2)=0','x','y'); >> [x y] ans = [ 0, 0] [ (2 + 2*2^(1/2)*i)^(1/2)/2 - (2 + 2*2^(1/2)*i)^(3/2)/4, (2 + 2*2^(1/2)*i)^(1/2)] [ (2 - 2*2^(1/2)*i)^(1/2)/2 - (2 - 2*2^(1/2)*i)^(3/2)/4, (2 - 2*2^(1/2)*i)^(1/2)] [ - (2 + 2*2^(1/2)*i)^(1/2)/2 + (2 + 2*2^(1/2)*i)^(3/2)/4, -(2*2^(1/2)*i + 2)^(1/2)] [ - (2 - 2*2^(1/2)*i)^(1/2)/2 + (2 - 2*2^(1/2)*i)^(3/2)/4, -(2 - 2*2^(1/2)*i)^(1/2)]
(2) >> syms x y >> [x y]=solve('-x+x^3+x*y^2=0','-y+y^3+x^2*y=0'); >> [x y] ans = [ 0, 0] [ 1, 0] [ 0, 1] [ 0, -1] [ -1, 0] [ -(1 - z^2)^(1/2), z] [ (1 - z^2)^(1/2), z] (5) syms x y [x y]=solve('y*cos(xபைடு நூலகம்=0','sin(x)=0'); >> [x y] ans = [ 0, 0]