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Systems of dynamical interactions between competing species can be used tomodel many complex systems, and can be mathematically described by {\em random}networks. Understanding how patterns of activity arise in such systems isimportant for understanding many natural phenomena. The emergence of patternsof activity on complex networks with reaction-diffusion dynamics on the nodesis studied here. The connection between solutions with a single activated node,which can bifurcate from an undifferentiated state, and the fully developedsystem-scale patterns are investigated computationally. The differentcoexisting patterns of activity the network can exhibit are shown to beconnected via a snaking type bifurcation structure, similar to thoseresponsible for organising localised pattern formation in regular lattices.These results reveal the origin of the multistable patterns found in systemsorganised on complex networks. A key role is found to be played by nodes withso called {\em optimal degree}, on which the interaction between the reactionkinetics and the network structure organise the behaviour of the system. Astatistical representation of the density of solutions over the parameter spaceis used as a means to answer important questions about the number of accessiblestates that can be exhibited in systems with such a high degree of complexity.

Pattern Formation on Networks: from Localised Activity to Turing Patterns