Periodic solutions of differential-difference equations as plane cycles (Q2783622)

Periodic solutions to the functional recurrence NEWLINE\[NEWLINEdx_{n+1}/dt=F(x_n,x_{n+1}), \quad x_n(\tau)=x_{n+1}(0), \quad x_{N+1}=x_1,NEWLINE\]NEWLINE are interpreted as closed plane curves satisfying a suitable differential problem. The Hopf bifurcation of constant solutions gives rise to a continuous family of such curves which, for \(N\to\infty\) , take the form of heteroclinic connections between the \(2-\)cycles of \(F(x,x')=0\). These heteroclinic connections are studied in the case \(F(x,y)=-y+f(x)\), with \(f\) decreasing.