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The advection of passive scalars in time-independent two-dimensional incompressible fluid flows is an integrable Hamiltonian system. It becomes non-integrable if the corresponding stream function depends explicitly on time, allowing the possibility of chaotic advection of particles. We consider for a specific model (double gyre flow), a given number of exits through which advected particles can leak, without disturbing the flow itself. We investigate fractal escape basins in this problem and characterize fractality by computing the uncertainty exponent and basin entropy. Furthermore, we observe the presence of basin boundaries with points exhibiting the Wada property, i.e., boundary points that separate three or more escape basins., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

We investigate periodicity suppression by an external periodic forcing in different flows, each modeled by a set of three autonomous nonlinear first-order ordinary differential equations. By varying the amplitude of a sinusoidal forcing with a fixed angular frequency, we show through numerical simulations, including parameter planes plots, phase-space portraits, and the largest Lyapunov exponent, that windows of periodicity embedded in chaotic regions may be totally suppressed.