Measure synchronization(Average bare energy and interaction energy)

Dear everyone, i need your assistance.

I'm currently working on my PhD dissertaion on measure synchronization. i have gotten the phase plot,time series,amplitude,Frequency,power,and also the poincare section.i really need your assistance on how to go with the Average bare energy and interaction energy.

my emial:[e-mail]...i would welcome any assistance...am greatful

Answer 1

[OGUNGBEMI Ezekiel]

this is the code i have tried for the

Exploring the route to measure synchronization in non-linearly coupled Hamiltonian systems journal..but its not running..

any advice or suggestion is welcome.

%% %% plotting coupling measure schronization for N=2

clear all; close all; clc; %#ok<CLALL>

y=[0:0.01:40];

m=length(y);

%tspan=[0:0.1:100];

E=0.2;

p1=0.2;

p2=sqrt(2*E - (p1)^2)

for i=1:m

[t{i},x{i}]= ode45(@(t,x) exploring(t,x,y(i)),[0 100],[0 0 p1 p2]);

end

%EX=(1/2).*(y*X(:,2).^2 * X(:,1).^2)

%S= trapz(EX);

%%

figure(1)

plot(X(:,1),X(:,3),'b',X(:,2),X(:,4),'r ')%y=0 together

figure(2)

subplot(1,2,1)

plot(X(:,1),X(:,3),'b');%y=0 seperate plots

subplot(1,2,2)

plot(X(:,2),X(:,4),'r');

figure(3)%y=0.007 together

plot(Y(:,1),Y(:,3),'b',Y(:,2),Y(:,4),'r ')

figure(4)%y=0.007 seperate plots

subplot(1,2,1)

plot(Y(:,1),Y(:,3),'b');

subplot(1,2,2)

plot(Y(:,2),Y(:,4),'r');

figure(5)%y=0.15 together

plot(W(:,1),W(:,3),'b',W(:,2),W(:,4),'r ')

figure(6)%y=0.15 seperate plots

subplot(1,2,1)

plot(W(:,1),W(:,3),'b');

subplot(1,2,2)

plot(W(:,2),W(:,4),'r');

figure(7)%y=0.52 together

plot(Z(:,1),Z(:,3),'b',Z(:,2),Z(:,4),'r ')

figure(8)%y=0.52 seperate plots

subplot(1,2,1)

plot(Z(:,1),Z(:,3),'b');

subplot(1,2,2)

plot(Z(:,2),Z(:,4),'r');

Answer 2

[OGUNGBEMI Ezekiel]

This is the code i did for myself for the average bare energy.

function dxdt = exploring(t,x,y)

dxdt = zeros(4,1);

dxdt(1) = x(3);

dxdt(2) = x(4);

dxdt(3) = -x(1) + y*x(1)*x(2^2);

dxdt(4) = -x(2) + y*x(1)^2*x(2);

%% %% Average bear energy

clear all; close all; clc; %#ok<CLALL>

y=[0 0.07 0.15 0.52];

m=length(y);

tspan=[500:0.001:1400];

T=0:0.01:1400

L=10;

E=0.2;

p1=0.2;

p2=sqrt(2*E - (p1)^2);

E1=((p1)^2 + y*(p1)^2)/2;

E2=((p2)^2 + y*(p2)^2)/2;

R =(1/ T) * integral((E1*E2),0,T);

for i=1:m

[t,R] = trapz(@(t,R) exploring(t,R,y(i)),tspan,[0 0 p1 p2]);

end

X=R{:,1};

Y=R{:,2};

W=R{:,3};

Z=R{:,4};

figure(1)

plot(X(:,1),X(:,3),'b',X(:,2),X(:,4),'r ')%y=0 together

this is what is given me as error

Error using /

Matrix dimensions must agree.

Error in bearenergy (line 13)

R =(1/ T) * integral((E1*E2),0,T);

thanks in anticipation.