Frustration induced chaos in a system of coupled ODEʹs

We investigate the behaviour of a system of up to six coupled ordinary differential equations (ODEʹs) which form a simple network. This paper addresses the question of the sensitivity of the network dynamics as a function of the symmetry properties of the connectivity of its units. The specific network to be studied is an immune idiotypic network in which the prevailing behaviour is oscillatory. It is shown that connecting the idiotypic network in a frustrated (i.e. closed chain) way transforms the oscillatory regime into a chaotic one. Standard analysis like the Lorentz first return map and power spectra together with recently appeared symbolic and statistical types of analysis are carried out in a general attempt to connect the frustration induced chaotic regime with other kinds of chaos. The main originality of this regime lies in the behavioural equivalence of the variables involved due to the homogeneity of the network structure of the system and the closed chain connectivity.