System of differential equations in Maple

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Hi everybody.

I'm using the Maple 13 software (in linux mint) to solve system compounded by the four below differential equations:

> ode1 := (diff(m1(t), t)) = - m1(t) + (1/2)*tanh( m2(t) + m4(t) + cos(t) );
> ode2 := (diff(m2(t), t)) = - m2(t) + (1/2)*tanh( m1(t) + cos(t) );
> ode3 := (diff(m3(t), t)) = - m3(t) + (1/2)*tanh( m4(t) + cos(t) );
> ode4 := (diff(m4(t), t)) = - m4(t) + (1/2)*tanh( m3(t) + m1(t) + cos(t) );Anyone knows how can I plot the "m1", "m2", "m3" and "m4" by the independent variable "t" ??

 

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Hi guys.

I found a way to solve the above problem. I didn't immediately plot the graphs, but I obtained the values of each greatness "mi(t)" through specific values of parametric variable "t". Below an example for t=0.8.

> restart;
> with(DEtools, DEplot);
> with(plots);
>
> # ode1 := diff(m1(t), t) = -m1(t)+(1/2)*tanh(m2(t)+m4(t)+cos(t));
> # ode2 := diff(m2(t), t) = -m2(t)+(1/2)*tanh(m1(t)+cos(t));
> # ode3 := diff(m3(t), t) = -m3(t)+(1/2)*tanh(m4(t)+cos(t));
> # ode4 := diff(m4(t), t) = -m4(t)+(1/2)*tanh(m3(t)+m1(t)+cos(t));
>
> dsys := {diff(m1(t), t) = -m1(t)+(1/2)*tanh(m2(t)+m4(t)+cos(t)), diff(m2(t), t) = -m2(t)+(1/2)*tanh(m1(t)+cos(t)), diff(m3(t), t) = -m3(t)+(1/2)*tanh(m4(t)+cos(t)), diff(m4(t), t) = -m4(t)+(1/2)*tanh(m3(t)+m1(t)+cos(t)),m1(0) = 0, m2(0) = 0, m3(0) = 0, m4(0) = 0};
> dsn1 := dsolve(dsys, numeric);
> dsn1(.8);
[t = 0.8, m1(t) = 0.225131111929745192, m2(t) = 0.211465317954931536, m3(t) = 0.211465317954931536, m4(t) = 0.225131111929745192]I expect this topic may be helpful.