We introduce a class of models composed by lattices of coupled complex-amplitude oscillators which preserve the norm. These models are particularly well adapted to investigate phenomena described by the nonlinear Schrödinger equation. The coupling between oscillators is parameterized by the...

We report exact analytical expressions locating the 0→1, 1→2 and 2→4 bifurcation curves for a prototypical system of two linearly coupled quadratic maps. Of interest is the precise location of the parameter sets where Naimark–Sacker bifurcations occur, starting from a non-diagonal...

We investigate the parameter space of two coupled quadratic (logistic) maps. Of special interest is the analytical characterization of the precursors leading to riddled basins. We delimit stability domains for orbits with the two lowest periods. In addition, we study the singularities of the...

We show that dissipative dynamical systems with constant Jacobian allow one to recover numerical values of control parameters under which the system is operating. This is done by performing measurements on self-similar (fractal) structures in phase space. We illustrate parameter recovery...