Floquet bundles for tridiagonal competitive-cooperative systems and the dynamics of time-recurrent systems (Q2855136)

This interesting paper investigates nonautonomous tridiagonal competitive-cooperative ODEs of the form NEWLINE\[NEWLINE \dot x_1=f_1(t,x_1,x_2), \quad \dot x_i=f_i(t,x_{i-1},x_i,x_{i+1}), \quad \dot x_n=f_n(t,x_{n-1},x_n) NEWLINE\]NEWLINE with \(1<i<n\) and a quite general time-dependence.NEWLINENEWLINEIn the framework of skew-product flows, exponentially separated Floquet bundles are obtained for corresponding linear equations. The resulting Floquet theory is used to investigate the dynamics on the hyperbolic \(\omega\)-limit sets for general nonlinear systems of the above form. The related time-recurrent structures include almost periodicity and automorphy.