14 years, 6 days

## Thanks Giorgios! First of...

Thanks Giorgios! First of all, as you noted, a correction is needed x'=a*b*((x^2+c^2)/(x^2+1))-d*x y'=a*e*((y^3+f^3)/(x^3+1)*(g*x+1))-y initial cond. x(0)=y(0)=0.01 With the above source Maple plots a trajectory. O.K. But how colud I identify the bifurcations of the system by some parameter, say e? If there exist.. I obtained below the phase plane, hope it is correct > sys:=diff(x(t),t)=7*(0.2)*(((x(t))^2+(0.2)^2)/((x(t))^2+1))-(0.1)*(x(t)),diff(y(t),t)=7*15*(((y(t))^3+(0.5)^3)/(((y(t))^3+1)*((0.1)*x(t)+1)))-y(t): > p2:=DEplot({sys},[x(t),y(t)],t=-1..20,[[0,1.7,52],[0,5,40],[0,9.5,62],[0,10,30],[0,18,57],[0,18,28],[0,28,45],[0,24,21],[0,36,38],[0,35,17],[0,40,18],[0,40,25],[0,60,10],[0,63,1],[0,64,63]],stepsize=0.1,x=0..50,y=0..80,linestyle=6, linecolor=black,color=red,arrows=SLIM,title=phase_portrait): > p2:=subs(THICKNESS(3)=THICKNESS(2),[p2]): > display(p2,font=[TIMES,8],insequence=true); What are the functions for plotting or looking for bifurcations for nonlinear systems? Thanks again! carmina

## Thanks Giorgios! First of...

Thanks Giorgios! First of all, as you noted, a correction is needed x'=a*b*((x^2+c^2)/(x^2+1))-d*x y'=a*e*((y^3+f^3)/(x^3+1)*(g*x+1))-y initial cond. x(0)=y(0)=0.01 With the above source Maple plots a trajectory. O.K. But how colud I identify the bifurcations of the system by some parameter, say e? If there exist.. I obtained below the phase plane, hope it is correct > sys:=diff(x(t),t)=7*(0.2)*(((x(t))^2+(0.2)^2)/((x(t))^2+1))-(0.1)*(x(t)),diff(y(t),t)=7*15*(((y(t))^3+(0.5)^3)/(((y(t))^3+1)*((0.1)*x(t)+1)))-y(t): > p2:=DEplot({sys},[x(t),y(t)],t=-1..20,[[0,1.7,52],[0,5,40],[0,9.5,62],[0,10,30],[0,18,57],[0,18,28],[0,28,45],[0,24,21],[0,36,38],[0,35,17],[0,40,18],[0,40,25],[0,60,10],[0,63,1],[0,64,63]],stepsize=0.1,x=0..50,y=0..80,linestyle=6, linecolor=black,color=red,arrows=SLIM,title=phase_portrait): > p2:=subs(THICKNESS(3)=THICKNESS(2),[p2]): > display(p2,font=[TIMES,8],insequence=true); What are the functions for plotting or looking for bifurcations for nonlinear systems? Thanks again! carmina
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