  Nonlinear instabilities are responsible for spontaneous pattern formation in
a vast number of natural and engineered systems ranging from biology to
galaxies build-up. We propose a new instability mechanism leading to pattern
formation in spatially extended nonlinear systems based on a periodic antiphase
modulation of spectrally-dependent losses arranged in a zig-zag way: an
effective filtering is imposed at symmetrically located wavenumbers k and -k in
alternating order. The properties of the dissipative parametric instability
differ from the features of the both key classical concepts of modulation
instabilities: the Benjamin-Feir, and the Faraday instability. We demonstrate
how dissipative parametric instability can lead to the formation of stable
patterns in one and two-dimensional systems. The proposed instability mechanism
is generic and can naturally occur or can be implemented in various physical
systems.
