Chaos and hyperchaos in fractional-order cellular neural networks

In this paper, a fractional-order four-cell cellular neural network is proposed and the complex dynamical behaviors of such a network are investigated by means of numerical simulations. Several varieties of interesting dynamical behaviors, such as periodic, chaotic and hyperchaotic motions, are displayed. In addition, it can be found that the network does exhibit hyperchaotic phenomena over a wide range of values of some specified parameter. The existence of chaotic and hyperchaotic attractors is verified with the related Lyapunov exponent spectrum, bifurcation diagram and phase portraits. Meanwhile, the Lyapunov exponents and Poincaré sections are calculated for some typical parameters, respectively.