A Systematic Approach to Bi-Directionally Nonlinearly Coupled Systems Design for the Generation of Complex Dynamical Behaviours

In this paper, a procedure to design a class of coupled systems that exhibit complex behaviours is presented. The proposed method is rigorously and systematically applicable to any dynamic system with nonlinear polynomial elements. Starting from two identical nonlinear algebraic systems, the proposed approach determines a proper bidirectional coupling that is able to force the coupled systems to exhibit complex behaviours. The coupling strength permits to control bifurcations of the system, i.e., to move through different regions of the parameter space, characterized by different complex behaviours of the system. Among the analyzed complex phenomena (generalized synchronization, blowout bifurcation, on-off intermittency and hyperchaos) a particular relevance is given to hyperchaotic behaviour. Moreover the basic design principle is demonstrated by means of proper examples.