On the structural cycles in block random systems

Abstract

Block random model was introduced to study the behavior of large complicated systems [6]. Lability index was used for measuring instability. It was shown that a smaller system is more stable than a larger one with the same parameters. Thus crisis cycles can be perceived in strong changes of the number of participants. In the present paper we study the behavior of a block random model with constant number of participants. Here one can observe the so called structural cycles. They consist of two parts: a so called convergence period and a so called divergence period, which are mentioned together as structural cycles, the length of it is structural cycle time. We show that a proportionally larger density matrix and dispersion result in a shorter cycle time, meanwhile lability indices of systems are the same. Further, it is seen that dispersion plays crucial role in specifying stability, while density matrix can only modify it. As a consequence, one can observe that longer cycle time can make it possible for the participants to adapt themselves to the circumstances and so to avoid that structural cycles turn into crisis cycle of the original nonlinear system.