Hello,

I would like to plot an non coupled non linear oscillator.

The equations are the following:

**K:=Matrix([<0, -1, 1, -1>,<-1, 0, -1, 1>,<-1, 1, 0,-1>,<1, -1, -1,0>]);**

**omega[sw]:=beta/(1-beta)*omega[s];**

**for i to 4**

**do **

**r[i]:=sqrt((u[i](t)/(L/2))^2+(v[i](t)/H)^2):**

**omega[i]:=omega[st]/(1+exp(b*v[i](t)))+omega[sw]/(1+exp(-b*v[i](t))):**

**Equ[i]:=diff(u[i](t),t)=Au*(1-r[i]^2)*u[i](t)+omega[i]*(L/2)/H*v[i](t):**

**Eqv[i]:=diff(v[i](t),t)=Av*(1-r[i]^2)*v[i]+omega[i]*(L/2)/H*v[i](t)+MatrixVectorMultiply(K,<seq(v[i](t),i=1..4)>)[i]:**

**EqSys[i]:=[Equ[i],Eqv[i]]:**

**end do:**

My parameters are the following:

**paramsGeo:=L=0.015,H=0.015,beta=0.5,Vf=0.3;**

**omegaS:=eval(Pi*Vf/L, [paramsGeo]);**

**paramsCycle:=omega[s]=omegaS,Au=1,Av=1,b=100;**

**params:=paramsGeo,paramsCycle;**

I'm not sure with my initial equations. But, may be it is possible to start with:

ic:=[u[1](0)=0.8, v[1](0)=0,u[2](0)=0.8, v[2](0)=0,u[3](0)=0.8, v[3](0)=0,u[4](0)=0.8, v[4](0)=0];

For these equations, I would like to obtain the following plots:

- plot 1: horizontal axis : u[1](t) vertical axis : v[1](t).

- plot 2: horizontal axis : u[2](t) vertical axis : v[2](t).

- plot 3: horizontal axis : u[3](t) vertical axis : v[3](t).

- plot 4: horizontal axis : u[4](t) vertical axis : v[4](t).

- plot 5: horizontal axis : t, vertical axis : v[1](t), v[2](t), v[3](t), v[4](t).

For this last plot, I would like to obtain this kind of curve:

I image that since my equations are coupled i can not use directly use Deplot function but Dsolve.

**May you help me for defining a good syntax for solving my system and then deducing the following plots?**

Thanks a lot for your help