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These are questions asked by gvelbu12

Find the solution by using fsolve?...

gvelbu12 5 Maple
July 05 2016
0 2

Table_1_for_example_1.mw

I am try to find root by using fsolve. But I am not get solution.

Please help me to solve this problem?

I have been attached the program above.

Thank You.

Best Regards.

Velmurugan G

 

 

How to find root for equation with 'w'?...

gvelbu12 5 Maple 18
rootfinding fsolve
June 08 2016
0 4


Here, I attached my maple code. I need to find root. I am using fsolve. But I am not geting the root. Please any one help me... to find the root.

> 

reatart:NULL``
> 

m1 := 0.3e-1;

0.3e-1

 (1)
> 

m2 := .4;

.4

 (2)
> 

m3 := 2.5;

2.5

 (3)
> 

m4 := .3;

.3

 (4)
> 

be := .1;

.1

 (5)
> 

rho := .1;

.1

 (6)
> 

ga := 25;

25

 (7)
> 

a := 3.142;

3.142

 (8)
> 

q := .5;

.5

 (9)
> 

z[0] := 3;

3

 (10)
> 

x[0] := 1.5152;

1.5152

 (11)
> 

w[0] := 1.1152;

1.1152

 (12)
> 

a1 := be*z[0];

.3

 (13)
> 

a2 := be*x[0];

.15152

 (14)
> 

a3 := rho*w[0];

.11152

 (15)
> 

a4 := rho*z[0];

.3

 (16)
> 

a5 := rho*w[0];

.11152

 (17)
> 

a6 := rho*z[0];

.3

 (18)
> 

b1 := a1*a4*ga+a4*ga*m1;

2.475

 (19)
> 

D1 := a1+m1+m2+m3+m4;

3.53

 (20)
> 

D2 := a1*m2+a1*m3+a1*m4-a2*ga+a3*ga+m1*m2+m1*m3+m1*m4+m2*m3+m2*m4+m3*m4;

1.92600

 (21)
> 

D3 := a1*a3*ga+a1*m2*m3+a1*m2*m4+a1*m3*m4-a2*ga*m1-a2*ga*m4+a3*ga*m1+a3*ga*m4+m1*m2*m3+m1*m3*m4+m2*m3*m4+m1*m2*m3;

1.4499000

 (22)
> 

D4 := a1*a3*a4*ga+a1*m2*m3*m4-a2*ga*m1*m4+a3*ga*m1*m4+m1*m2*m3*m4;

.3409200

 (23)
> 

G1 := -a1*a6-a6*m1-a6*m2-a6*m3;

-.969

 (24)
> 

G2 := -a1*a6*m2-a1*a6*m3+a2*a6*ga-a3*a6*ga+a4*a5*ga-a6*m1*m2-a6*m1*m3-a6*m2*m3;

.549300

 (25)
> 

G3 := -a1*a3*a6*ga-a1*a6*m2*m3+a2*a6*ga*m1-a3*a6*ga*m1-a6*m1*m2*m3;

-.3409200

 (26)
> 

A1 := w^(4*q)*cos(4*q*a*(1/2))+D1*w^(3*q)*cos(3*q*a*(1/2))+D2*w^(2*q)*cos(2*q*a*(1/2))+D3*w^q*cos((1/2)*q*a)+D4;

-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200

 (27)
> 

B1 := w^(4*q)*sin(4*q*a*(1/2))+D1*w^(3*q)*sin(3*q*a*(1/2))+D2*w^(2*q)*sin(2*q*a*(1/2))+D3*w^q*sin((1/2)*q*a);

-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5

 (28)
> 

A2 := -w^(3*q)*a6*cos(3*q*a*(1/2))+G1*w^(2*q)*cos(2*q*a*(1/2))+G2*w^q*cos((1/2)*q*a)+G3;

.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200

 (29)
> 

B2 := -w^(3*q)*a6*sin(3*q*a*(1/2))+G1*w^(2*q)*sin(2*q*a*(1/2))+G2*w^q*sin((1/2)*q*a);

-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5

 (30)
> 

C := .27601200;

.27601200

 (31)
> 

Q1 := 4*C^2*(A2^2+B2^2);

.3047304966*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2

 (32)
> 

Q2 := -4*C*A2*(A1^2-A2^2+B1^2-B2^2-C^2);

-1.10404800*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)*((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)

 (33)
> 

Q3 := (A1^2-A2^2+B1^2-B2^2-C^2)^2-4*C^2*B2^2;

((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)^2-.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2

 (34)
> 

V := simplify(-4*Q1*Q3+Q2^2);

-0.1e-12-0.5481797400e-1*w^11-40.93358002*w^(19/2)-212.0102604*w^(17/2)-1.048226159*w^(21/2)-8.667039897*w^10-119.4464160*w^9-208.1803245*w^8-54.3436016*w^7-38.4722894*w^6+2.67061391*w^5-2.29413863*w^4-.136247212*w^2+.899997750*w^3+0.1e-10*w^(1/2)-0.150073928e-1*w^(3/2)+0.54469063e-2*w-2.53869438*w^(11/2)-2.40374793*w^(9/2)-84.14780373*w^(15/2)-86.62603442*w^(13/2)+2.023073705*w^(7/2)-0.6906749e-2*w^(5/2)

 (35)
> 

x := (-Q2+sqrt(V))/(2*Q1);

(1/2)*(1.10404800*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)*((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)+(-0.1e-12-0.5481797400e-1*w^11-40.93358002*w^(19/2)-212.0102604*w^(17/2)-1.048226159*w^(21/2)-8.667039897*w^10-119.4464160*w^9-208.1803245*w^8-54.3436016*w^7-38.4722894*w^6+2.67061391*w^5-2.29413863*w^4-.136247212*w^2+.899997750*w^3+0.1e-10*w^(1/2)-0.150073928e-1*w^(3/2)+0.54469063e-2*w-2.53869438*w^(11/2)-2.40374793*w^(9/2)-84.14780373*w^(15/2)-86.62603442*w^(13/2)+2.023073705*w^(7/2)-0.6906749e-2*w^(5/2))^(1/2))/(.3047304966*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2)

 (36)
> 

E := -2*A1*C*x-A1^2+A2^2-B1^2+B2^2-C^2;

-.2760120000*(-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)*(1.10404800*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)*((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)+(-0.1e-12-0.5481797400e-1*w^11-40.93358002*w^(19/2)-212.0102604*w^(17/2)-1.048226159*w^(21/2)-8.667039897*w^10-119.4464160*w^9-208.1803245*w^8-54.3436016*w^7-38.4722894*w^6+2.67061391*w^5-2.29413863*w^4-.136247212*w^2+.899997750*w^3+0.1e-10*w^(1/2)-0.150073928e-1*w^(3/2)+0.54469063e-2*w-2.53869438*w^(11/2)-2.40374793*w^(9/2)-84.14780373*w^(15/2)-86.62603442*w^(13/2)+2.023073705*w^(7/2)-0.6906749e-2*w^(5/2))^(1/2))/(.3047304966*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2)-(-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2+(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2-(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2+(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1

 (37)
> 

y := -E/(2*C*B1);

-1.811515442*(-.2760120000*(-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)*(1.10404800*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)*((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)+(-0.1e-12-0.5481797400e-1*w^11-40.93358002*w^(19/2)-212.0102604*w^(17/2)-1.048226159*w^(21/2)-8.667039897*w^10-119.4464160*w^9-208.1803245*w^8-54.3436016*w^7-38.4722894*w^6+2.67061391*w^5-2.29413863*w^4-.136247212*w^2+.899997750*w^3+0.1e-10*w^(1/2)-0.150073928e-1*w^(3/2)+0.54469063e-2*w-2.53869438*w^(11/2)-2.40374793*w^(9/2)-84.14780373*w^(15/2)-86.62603442*w^(13/2)+2.023073705*w^(7/2)-0.6906749e-2*w^(5/2))^(1/2))/(.3047304966*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2)-(-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2+(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2-(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2+(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)/(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)

 (38)
> 

``
> 

fsolve(x^2+y^2 = 1, w)

fsolve((1/4)*(1.10404800*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)*((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)+(-0.1e-12-0.5481797400e-1*w^11-40.93358002*w^(19/2)-212.0102604*w^(17/2)-1.048226159*w^(21/2)-8.667039897*w^10-119.4464160*w^9-208.1803245*w^8-54.3436016*w^7-38.4722894*w^6+2.67061391*w^5-2.29413863*w^4-.136247212*w^2+.899997750*w^3+0.1e-10*w^(1/2)-0.150073928e-1*w^(3/2)+0.54469063e-2*w-2.53869438*w^(11/2)-2.40374793*w^(9/2)-84.14780373*w^(15/2)-86.62603442*w^(13/2)+2.023073705*w^(7/2)-0.6906749e-2*w^(5/2))^(1/2))^2/(.3047304966*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2)^2+3.281588197*(-.2760120000*(-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)*(1.10404800*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)*((-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2-(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2-(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)+(-0.1e-12-0.5481797400e-1*w^11-40.93358002*w^(19/2)-212.0102604*w^(17/2)-1.048226159*w^(21/2)-8.667039897*w^10-119.4464160*w^9-208.1803245*w^8-54.3436016*w^7-38.4722894*w^6+2.67061391*w^5-2.29413863*w^4-.136247212*w^2+.899997750*w^3+0.1e-10*w^(1/2)-0.150073928e-1*w^(3/2)+0.54469063e-2*w-2.53869438*w^(11/2)-2.40374793*w^(9/2)-84.14780373*w^(15/2)-86.62603442*w^(13/2)+2.023073705*w^(7/2)-0.6906749e-2*w^(5/2))^(1/2))/(.3047304966*(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2+.3047304966*(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2)-(-.9999999170*w^2.0-2.496849400*w^1.5-0.3922745903e-3*w^1.0+1.025129710*w^.5+.3409200)^2+(.2121968329*w^1.5+0.1973593344e-3*w^1.0+.3883741982*w^.5-.3409200)^2-(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2+(-.2120672160*w^1.5-.9689999799*w^1.0+.3884533076*w^.5)^2-0.7618262414e-1)^2/(-0.4073463989e-3*w^2.0+2.495324242*w^1.5+1.925999960*w^1.0+1.025338523*w^.5)^2 = 1, w)

 (39)
> 

``

 

Download root.mw

Bifurcation plot for ODE system with del...

gvelbu12 5 Maple
plot homework bifurcation
May 10 2016
2 7

Consider the following dynamical systems with time delay:

diff(x(t), t) = y(t)-bx(t)^3+ax(t)^2-z(t-tau)+I

diff(y(t), t) = c-dx(t)^2-y(t)

diff(z(t), t) = r(s(x-beta)-z(t))

Here the values of the parameters are a = 3, b = 1, c = 1, d = 5, s = 4, beta = 1.6, r = 0.6e-2, I = 3.0

 

Please help me 

How to write code for bifurcation plot for the above differential equations with delay.

Delay as taken as bifurcation parameter.

 

Reply message is very useful.

 

Thanks in Advance

 

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