We investigate the interaction of stationary and oscillatory dissipative solitons in the framework of two coupled cubic-quintic complex Ginzburg-Landau equation for counter-propagating waves. We analyze the case of a stabilizing as well as a destabilizing cubic cross-coupling between the counter-propagating dissipative solitons. The three types of interacting localized solutions investigated are stationary, oscillatory with one frequency, and oscillatory with two frequencies. We show that there is a large number of different outcomes as a result of these collisions including stationary as well as oscillatory bound states and compound states with one and two frequencies. The two most remarkable results are (a) the occurrence of bound states and compound states of exploding dissipative solitons as outcome of the collisions of stationary and oscillatory pulses; and (b) spatiotemporal disorder due to the creation, interaction, and annihilation of dissipative solitons for colliding oscillatory dissipative solitons as initial conditions.
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