Analytical Criteria for the Local Activity of Three-Port CNN with Five State Variables: Analysis and Application

The local activity principle of the cellular nonlinear network(CNN) introduced by Chua has provided a powerful tool for studying the emergence of complex patterns in a homogeneous lattice formed by coupled cells. This paper presents some analytical criteria for the local activity of three-port CNN with five state variables. As an application, a coupled CNN is introduced, whose prototype is the 5-dimensional differential equations for the interaction of T cells with antigen presenting cells (APCs) presented by Fishman and Perelson. Using the analytical criteria this paper calculates the bifurcation diagram of the APC CNN. Although no chaotic phenomena have been identified in simulations, many complex dynamical behaviors have been observed at or nearby the edge of chaos. Numerical simulations show once again that the emergence may exist if the selected cell parameters are nearby the edge of chaos domain.