FRUSTRATION INDUCED CHAOS IN A SYSTEM OF COUPLED ODES

We investigate the behaviour of a system of up to six coupled ordinary differential equations (ODE's) which form a simple network. This pape r addresses the question of the sensitivity of the network dynamics as a function of the symmetry properties of the connectivity of its unit s. The specific network to be studied is an immune idiotypic network i n which the prevailing behaviour is oscillatory. It is shown that conn ecting the idiotypic network in a frustrated (i.e. closed chain) way t ransforms the oscillatory regime into a chaotic one. Standard analysis like the Lorentz first return map and power spectra together with rec ently appeared symbolic and statistical types of analysis are carried out in a general attempt to connect the frustration induced chaotic re gime with other kinds of chaos. The main originality of this regime li es in the behavioural equivalence of the variables involved due to the homogeneity of the network structure of the system and the closed cha in connectivity.