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We introduce a discrete lossy system, into which a double hot spot (HS) isinserted, i.e., two mutually symmetric sites carrying linear gain and cubicnonlinearity. The system can be implemented as an array of optical or plasmonicwaveguides, with a pair of amplified nonlinear cores embedded into it. We focuson the case of the self-defocusing nonlinearity and cubic losses acting at theHSs. Symmetric localized modes pinned to the double HS are constructed in animplicit analytical form, which is done separately for the cases of odd andeven numbers of intermediate sites between the HSs. In the former case, somestationary solutions feature a W-like shape, with a low peak at the centralsite, added to tall peaks at the positions of the embedded HSs. The specialcase of two adjacent HSs is considered too. Stability of the solution familiesagainst small perturbations is investigated in a numerical form, which revealsstable and unstable subfamilies. The instability of symmetric modes accountingfor by an isolated positive eigenvalue leads to their spontaneoustransformation into co-existing stable antisymmetric modes, while theinstability represented by a pair of complex-conjugate eigenvalues gives riseto persistent breathers.

Symmetric and antisymmetric nonlinear modes supported by dual local gain in lossy lattices