A chaos-generator: analyses of complex dynamics of a cell equation in delayed cellular neural networks

Complex dynamics of a single delayed cellular neural cell equation with nonmonotone increasing output equation are investigated. Dynamic phenomena are analyzed in separate regions and bifurcation phenomena are displayed. It shows that this very simple cell exhibits various types of dynamical behaviors, including chaos. It turns out that for any given delay, there must exist parameter regions in which the cell is chaotic. Some conditions for chaos to exist are discussed. The presented model can serve as a chaos-generator, in which chaos can be generated from any one-dimensional (1-D) linear autonomous system just by the addition of a piecewise-linear delayed feedback.