In the study [1], we considered a system of the form where K : R n → R n is a continuously differentiable function. We supposed that system (1.3) possesses an orbitally stable limit cycle and perturbed it with solutions of a chaos generating system, in the form of (1.1), and set up the system where µ is a nonzero number and M : R m → R n is a continuous function. The extension of sensitivity and chaos through period-doubling cascade for the coupled system (1.1)-(1.4) were rigorously proved in the paper [1]. As a result, we achieved chaotic cycles , that is, motions which behave cyclically and chaotically, simultaneously. The rich experience of chaos expansion in finite dimensional spaces provides a confidence that our approach mentioned in [1] has to work also in infinite dimensional spaces. In this paper, we numerically observe the presence of orbitally stable limit cycles in the 2 $_{−}$dimensional projections of the infinite dimensional space as well as their deformation to chaotic cycles under chaotic perturbations. By using the technique presented in [1], one can elaborate the results of the present study from the theoretical point of view. Although couplings of GDS systems have not been performed in the literature yet, our results reveal the opportunity of chaos extension in such systems. Summarizing, electronic systems are important tools for synchronization and chaos extension. In this paper, we make use of our previous approach [1] to extend chaos in unidirectionally coupled GDS systems. Our GDS was previously studied both theoretically and experimentally in [3], [52]-[66]. It represents a planar plasma layer coupled to a planar semiconductor layer, which are sandwiched between two planar electrodes to which a DC voltage is applied (see Fig. 1). We used one-dimensional fluid model for this system, where any pattern formation in the transversal direction is excluded and only the single dimension normal to the layers is resolved. For the gas discharge, the model takes into account electron and ion drift in the electric field, bulk impact ionization and secondary emission from the cathode as well as space charge effects. The semiconductor is approximated with a constant conductivity. The gas-discharge part of the model consists of continuity equations for two charged species, namely, 4 1.2 Description of the GDS system model u ′ = K ( u ) , (1.3) y ′ = K ( y ) + µM ( x ) , (1.4)