Scientists have explored the cosmic evolution of a generalized dilatonic ghost condensate field as a dark energy candidate. This model is formulated from a Lagrangian density featuring two dominant kinetic terms—one linear and one of arbitrary integer order $n>2$—combined with an exponential potential. The novelty lies in the field's interaction with dark matter via a source term, allowing for the study of the present universe under different coupling scenarios.

The study analyzed three situations: a non-interacting case ($Q=0$) and two specific interaction models ($Q\propto\rho_m\dot\varphi$ and $Q\propto\rho_m H$). For each model, a detailed phase-space analysis was performed to identify critical points and stability conditions. In all scenarios, the system reproduces standard cosmological dynamics, evolving towards late-time dark energy-dominated attractors, exhibiting quintessence or phantom features depending on the sign of the coupling parameter $\alpha$ associated with the standard kinetic term.

A joint likelihood analysis was conducted using Cosmic Chronometers, PantheonPlus, and DESI observations for two values of $n$ ($n=3$ and $n=5$). This allowed for the determination of marginalized parameter constraints at 68% and 95% confidence levels for the different $Q$-models. For the interaction term $Q\propto\dot\varphi\rho_m$, the direction of energy flow depends on the sign of $\alpha$. However, for $Q\propto H\rho_m$, the energy flow is consistently negative, indicating an energy transfer from dark matter to dark energy, irrespective of the sign of $\alpha$.