Frustrated chaos in biological networks

The behaviour of three biologically inspired networks is investigated: Immune Idiotypic Network (IIN), Hopfield Network (HN) and Coupled Map Lattice (CML), mainly the effect on the dynamics induced by connecting the network in a frustrated way. Frustration occurs when the global structure is such that local connectivity patterns responsible for stable behaviour are intertwined, leading to mutually competing attractors and chaotic itinerancy among brief appearance of these attractors. Frustration destabilizes the network and provokes an unpredictable ''wavering'' among the stable dynamic regimes which characterize the same network when it is interconnected in a non-frustrated way. As the main contribution of this paper, an immune idiotypic network in which the prevailing behaviour is oscillatory is studied in detail. It is shown how connecting an elementary three-clone network in a frustrating way transforms the oscillatory regime into a chaotic one. This chaotic regime is further analysed and several interesting aspects are discussed such as the variable homogeneity, the intrinsic chaotic itinerancy among brief oscillatory regimes and the strong unpredictability. In addition, dynamical regimes obtained by frustrating the connectivity of HN and CML are presented and the similarities as well as the differences with the INN dynamics are emphasized. Common to all these networks is the description of the frustrated chaos as a succession of attempts to relax the network into one of the oscillatory regimes given by a weaker and non-frustrated connectivity, an impossible achievement making the dynamics rambling over brief but repelling orbits. (C) 1997 Academic Press Limited.